Wenger turned down the chance to bring the former Gunners captain back to the Emirates Stadium before his eventual move to Stamford Bridge.
"It was the kind of relationship I always would have liked to keep," Fabregas told The Sun.
"On his birthdays, for his 1,000th game, he always had a text message from me. But I don't expect anything from anyone in life, positive or negative.
"But I'm sure once everything dies down a bit in the future we will talk. There is no problem. I'll always be grateful to him whatever happens."
Chelsea, currently top of the Premier League, travel to Manchester City on Sunday.