I would only do so at this juncture, if your daughter knows what you have offered and is able to accept it.
Frankly, I think you would be well advised to reconsider and offer financial help instead.
Letting your ex SIL live somewhere else and come to yours for dinner once a week, bringing his washing with him, if he has no washing-machine where he lives, might well be a better idea, than letting him move in.
I would tend to doubt that the break-up has been caused purely because of what you have mentioned here. Surely, even in this day and age, no-one divorces solely because his wife has started going out more? Or divorces because her husband won't do so?
The important thing here, as there are children involved, is to establish as amicable a relationship between the divorcing spouses as possible, and between each of them to the other members of the family.
This can usually be done if there is no violence or abuse involved as reasons for the divorce. Doing so, however, demands tact and an open discussion between you and your daughter regarding your wish to still be able to see your ex SIL. Such a discussion is probably more likely to succeed if he is not actually living in your house.
If he does move in, where is he supposed to go if your daughter drops in for a chat with you, or their children come visiting?