Just as it is not permissible for a man to wear natural silk, it is also not permissible for him to sit or sleep on it or to cover himself in it (like a blanket), because of the report narrated by al-Bukhaari (5837) from Hudhayfah (may Allah be pleased with him) who said: The Prophet (blessings and peace of Allah be upon him) forbade us to wear silk and brocade and to sit on them. 

Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: 

The words “and to sit on them” are strong proof for those who say that it is not allowed to sit on silk, which is the view of the majority. Ibn Wahb narrated in his Jaami‘ from the hadeeth of Sa‘d ibn Abi Waqqaas that he said: To sit on a live coal is dearer to me than sitting on a seat of silk. End quote. 

Ibn al-Qayyim (may Allah have mercy on him) said: 

Even if we did not have this text, the prohibition on wearing it would still include using it in furnishings, as it also includes using it as covers or blankets, as the word libs (lit. wearing) includes these meanings in both the linguistic and shar‘i sense; Anas said: I went to a reed mat of ours that had turned black from long use (lit. wearing). Narrated by al-Bukhaari (380) and Muslim (658). Even if the general wording did not imply that the prohibition included using it in furnishings, mere analogy would imply that it was forbidden. End quote. 

I‘laam al-Muwaqqi‘een, 2/366 

Al-Nawawi (may Allah have mercy on him) said in al-Majmoo‘, 4/321: 

It is haraam for a man to use brocade and silk in clothing, or for sitting or reclining on, or covering himself with it (like a blanket), or as a curtain or screen, or any other way of using it. There is no difference of scholarly opinion concerning any of these things except one odd view which was narrated by al-Raafi‘i, who said that it is permissible for them to sit on it. But this view is invalid and is clearly mistaken and is contrary to this saheeh hadeeth. This is our view. As for wearing it, there is consensus (that it is forbidden); with regard to other uses, Abu Haneefah permitted it but Maalik, Ahmad, Muhammad, Dawood and others agreed with us that it is forbidden. Our evidence for that is the hadeeth of Hudhayfah. Perhaps the reason for the prohibition on wearing it is to be found in the other ways of using it, because if it is forbidden to wear it when there is a need for it, then it is more likely to be forbidden in other cases. End quote. 

It says in al-Mawsoo‘ah al-Fiqhiyyah, 5/278: 

The fuqaha’ are unanimously agreed that it is permissible for women to use silk furnishings, but in the case of men, the majority of Maalikis, Shaafa‘is and Hanbalis are of the view that it is forbidden. End quote. 

Shaykh Saalih al-Fawzaan was asked: What is the ruling on using blankets, covers or furnishings made of silk? He replied: It is not permissible for them to use covers and furnishings made of silk, because Allah forbade it to men. End quote. 

Al-Muntaqa min Fataawa al-Fawzaan, 7/95. 

It should be pointed out that what is forbidden is natural silk, not artificial silk. For more information please see the answer to question no. 30812. 

Based on that, if this cover is made of natural silk, it is not permissible for you to sit or sleep on it. 

And Allah knows best.