Thibaut Courtois’ move to the Santiago Bernabeu over the summer has quashed those rumours, but the likes of Paris Saint-Germain and Juventus are now reported to be keen on landing a proven goalkeeper .
De Gea, who has enjoyed a record-setting seven-year spell in England , has offered no indication that he is looking to move on.
But with no extension having been agreed to a deal which will run to 2020 once a 12-month option is taken up , the 28-year-old’s former coach admits he may be considering a switch.
Steele, who left Old Trafford in the wake of David Moyes’ arrival in 2013, told the Goalkeepers’ Union podcast: "If you ask David now, he is fully committed to Manchester United.
"He has got a fantastic rapport with the players, the fans but he wants to be a winner and inevitably he might look at his pathway now and think 'will I get that at Manchester United', certainly at the moment they are still in the Champions League.
"But he sees other clubs getting bigger and stronger, it is becoming more competitive. And he is now 28, is coming into his prime years so it is understandable that he may be looking.
"But until somebody tells me he is leaving I think he will be fully committed.
"Long may David stay in the Premier League and long may he continue but you would understand why if he wants to win that ultimate prize. The one thing that's missing is he wants to win that Champions League.
"Will he be gaining that at Manchester United? I hope he does, I really do for the sake of the club because when you have been at somewhere like Manchester United you cannot stop being a supporter just when you leave it.
"So ideally I want him to stay and give great value to Manchester United and to the Premier League."
De Gea, who joined United in 2011, has made over 330 appearances for the Red Devils.
He has won the Premier League, FA Cup, League Cup, Community Shield and Europa League during his time in England and is widely considered to be one of the finest goalkeepers in world football .