It should be noted that one of the essential parts of khula‘, without which it is not valid, is the pronouncing of the word khula‘ or words that have the same meaning, whether that is explicit or implicit. It is essential that the husband pronounce the word khula‘ or words that carry the same meaning, so that the ruling may be applied and its consequences follow on. 

It says in al-Mawsoo‘ah al-Fiqhiyyah (19/245): According to scholars other than the Hanafis, there are five essential parts of khula‘: moojib, qaabil, mu‘awwad, ‘iwad and seeghah. 

The moojib (the one who issues the khula‘) is the husband.

The qaabil (the one who guarantees compensation) is the one who is committed to pay compensation.

The mu‘awwad (the thing for which compensation is given in return for giving it up) is intimacy with the wife.

The ‘iwad (what is agreed upon in return for foregoing the right to intimacy) is the thing in return for which khula‘ is given

The seeghah is the wording by which khula‘ takes place. 

With regard to the offer of khula‘ and acceptance thereof, these are essential parts of khula‘ according to the Hanafis, if khula‘ is in return for compensation. With regard to both, it is stipulated – as was stated by the Shaafa‘is – that the husband begins with an offer of exchange, such as saying “I offer you khula‘ in return for such and such.” Acceptance is done by uttering words on the part of one who can speak, or by gestures or writing in the case of one who cannot speak (non-verbal). There should be no discussion of different matters, in between the offer and acceptance, on the part of the one who is expected to give an answer; however, a little general talk is allowed. End quote. 

See the answer to question no. 191484 

Shaykh as-Sa‘di (may Allah have mercy on him) said: If they have agreed on khula‘ but have not done it yet – rather they only agreed that he will give her khula‘ if she gives him compensation – this does not count as an annulment of the marriage. Rather it is only a promise from him to annul it. If he has not yet annulled it, he may change his mind and not do it. End quote. 

Fataawa al-Mar’ah al-Muslimah, 2/785; fatwa from Shaykh ‘Abd ar-Rahmaan as-Sa‘di. 

Based on that: 

If the conditions of khula‘ are fulfilled by both husband and wife, and he has indeed uttered the word of khula‘, then it is not permissible for the wife to let the husband be intimate with her because she is completely divorced from him [and if they want to remarry they must do a new marriage contract]. 

But if the conditions of khula‘ have not been met – rather it is only an agreement and a promise, and the husband has not uttered the word of khula‘, or the qaadi (judge) has not yet decreed it – then she is still his wife and she may allow him to be intimate with her. Who knows, perhaps that will lead to them wanting to stay together and reconcile. 

And Allah knows best.