It is quite possible that he will decide to stay in Serie A, and I don't see any reason why he would want to go back to Manchester United now, firstly they refused to extend his contract, secondly their position in the Premier League is terrible, so De Gea might not be interested in this offer either.
Man U is indecisive and confused, why would they want to get back De Gea? goal keepers are meant to be kept aside or benched, not allowed to leave. Onana's underperformance has shown them the value of who they rejected. The management is begining to say it was a mistake to let De Gea go, but it's quite late. It's better to check on a young goal keeper that'll replace Onana.