The 31-year-old is into his eleventh season with the Red Devils, having joined from Atletico Madrid in the summer of 2011.
De Gea’s contract expires next summer, though the club have the option to extend it by a further year.
The Spain international has transformed into one of the best goalkeepers in world football since joining United.
As he prepares to meet his former employers for the first time since leaving in the UEFA Champions League on Wednesday, De Gea has given an indication that he will be extending his stay in the red half of Manchester.
"I like the fact I was born in Madrid, but at the end of the day, it's just a city," he told UEFA.
"Now I feel as if I'm from Manchester. I just feel like anyone else from Manchester. Where you are loved and welcomed is your home.
"I've been here for many years and, obviously, anything can happen in life, in the world of football, but honestly I don't see myself away from Manchester United.
"Of course, I'm going back home [for this tie], I'm going back to the club that gave me the opportunity to be who I am today. But this is just another match.
"Everyone wants to play well, we want to win, it is a Champions League match. Obviously, I wish Atletico all the best, but I don't know whether the fact we're playing them is a good or bad omen.
"Everyone is going there to win, especially me."
De Gea has won one Premier League title, one FA Cup, one League Cup and one Europa League in his time at Old Trafford.
