The view referred to in the question was suggested by al-Suyooti (may Allah have mercy on him) in his book al-Haawi, 2/249-256, in which he said that this world would last for seven thousand years and that the Prophet (peace and blessings of Allaah be upon him) was sent at the end of the sixth millennium. 

The end of the sixth millennium means half way through it. Based on that the lifespan of this ummah is more than one thousand years and less than 1500 years. 

He said: “The period cannot be fifteen hundred years at all.” 

I.e., the period must be less than fifteen hundred years. 

Then he mentioned the ahaadeeth and reports which he quoted as evidence to support that, some of which are Israa’eeliyyaat (reports from Jewish sources) which cannot be taken as evidence, and some of the rest are da’eef (weak), and the scholars ruled that they are lies and fabrications (mawdoo’). 

The evidence that this view is false includes the following: 

1 – If this view were correct, then everyone would know when the Hour is to begin. This goes against what is mentioned in the verses of the Qur’aan and the ahaadeeth of the Prophet (peace and blessings of Allaah be upon him) which definitely state that the time of the Hour is known to no one except Allaah. Allaah says (interpretation of the meaning): 

“People ask you concerning the Hour, say: ‘The knowledge of it is with Allaah only. What do you know? It may be that the Hour is near!’”

[al-Ahzaab 33:63]

Ibn Katheer said (6/527): 

Here Allaah tells His Messenger (peace and blessings of Allaah be upon him) that he has no knowledge of the Hour and that if people ask him about that, he should refer the matter to Allaah (i.e., say that only Allaah knows that). 

Al-Shanqeeti said (6/604): 

It is known that innama (translated here as “only”) conveys the meaning of exclusivity, so what the verse means is that the Hour is known only to Allaah alone. 

And Allaah says (interpretation of the meaning): 

“They ask you (O Muhammad) about the Hour — when will be its appointed time?

You have no knowledge to say anything about it. 

To your Lord belongs (the knowledge of) the term thereof?

You (O Muhammad) are only a warner for those who fear it”

[al-Naazi’aat 79:42-45]

Ibn Katheer (4/736) said: 

i.e., knowledge of that is not given to you or to anyone else in creation, rather the matter is to be referred to Allaah, for He is the One Who knows exactly when it will happen. 

Al-Sa’di said: Because knowledge of the Hour serves no religious or worldly purpose of people, rather their interests lie in its being hidden from them, the knowledge of that has been concealed from all of creation and Allaah has kept that knowledge to Himself. He says (interpretation of the meaning): 

“To your Lord belongs (the knowledge of) the term thereof?”

[al-Naaz’iaat 79:44]

The ahaadeeth which indicate that the time of the Hour is known only to Allaah include the famous hadeeth of Jibreel in which it says that the Prophet (peace and blessings of Allaah be upon him) said to Jibreel, when he asked him about the Hour: “The one who is asked about it does not know more than the one who is asking.” Narrated by Muslim, 8. 

2 – These reports which al-Suyooti (may Allaah have mercy on him) quoted as evidence were classed as da’eef (weak) by the scholars, and indeed they ruled that they were lies. 

Ibn al-Qayyim said in al-Manaar al-Muneef (1/80), where he mentions the ways in which a hadeeth may be known to be mawdoo’:  

“(one of these ways is): if the hadeeth goes against the clear meaning of the Qur’aan, such as the hadeeth which says that this world will last for seven thousand years and that we are now in the seventh millenium. This is one of the most obvious of lies. Because if it were correct then everyone would know that there was only two hundred and fifty-one years left until the Resurrection from our time [i.e., the time of Ibn al-Qayyim]. But Allaah says (interpretation of the meaning): 

“They ask you about the Hour (Day of Resurrection): “When will be its appointed time?” Say: “The knowledge thereof is with my Lord (Alone). None can reveal its time but He. Heavy is its burden through the heavens and the earth. It shall not come upon you except all of a sudden.” They ask you as if you have a good knowledge of it. Say: “The knowledge thereof is with Allaah (Alone)…”

[al-A’raaf 7:187]

Ibn Katheer said in al-Nihaayah fi’l-Fitan wa’l-Malaahim (1/25): 

There is no (sound) ahaadeeth in which the Prophet (peace and blessings of Allaah be upon him) defined when the Hour would be, rather he mentioned some of its portents and signs. 

He also said (2/28): 

With regard to the statements in the books of the Israa’eeliyyeen and the People of the Book which suggest that this world will last for a certain number of millennia, more than one of the scholars have stated that these are mistaken, and it comes as no surprise that they were mistaken. There is a hadeeth which says, “This world is one of the weeks of the Hereafter” but its isnaad is not saheeh either. The same applies to every hadeeth which states a specific time for the Day of Resurrection – none of their isnaads can be proven. 

Al-Sakhaawi said in al-Maqaasid al-Hasanah (p. 444): 

Everything that has been narrated describing a specific time for the Day of Resurrection either has no basis at all or its isnaad cannot be proven. 

3 – What al-Suyooti himself said indicates that this view is false. 

He mentions that the Mahdi will appear after twelve hundred years, but fourteen hundred years have passed and the Mahdi has not appeared yet. 

He says that people will remain for one hundred and twenty years after the sun rises from the west, then the Hour will begin. This means that the sun should have been rising from the west for more than twenty years!  

He says that the Dajjaal will appear after one hundred years, and the Messiah ‘Eesa ibn Maryam will come down and kill him, and he will remain after that for forty years, but here we are in the last century – according to what he says, and the Dajjaal has not appeared and the Messiah ‘Eesa ibn Maryam has not yet come down. 

He says that several of the major signs such as the Dajjaal, the descent of ‘Eesa and the rising of the sun from the west will happen more than two hundred years before the Hour begins. 

All of these things indicate that this view is false, and that knowledge of the Hour should be referred to Allaah, and Allaah commands us (interpretation of the meaning): 

“People ask you concerning the Hour, say: ‘The knowledge of it is with Allaah only. What do you know? It may be that the Hour is near!’”

[al-Ahzaab 33:63]

And Allaah knows best.