Arsenal are reportedly keen on attracting former Borussia Dortmund playmaker Mkhitaryan to Emirates Stadium as part of any agreement, with the Armenia global having come in for criticism from manager Jose Mourinho this season. However, the Mancunian giants want him to sign the new extension, as they wish to seal the deal before De Gea leaves for the World Cup at the end of the campaign.
De Gea has a deal until 2019, with United holding an option to extend it for another season.
Mkhitaryan has been linked with a move away from United after failing to win over Mourinho at Old Trafford this season.
Stoke were humbled in Mark Hughes' final game in charge at League Two Coventry City and, before handing over the reins to newly appointed boss Paul Lambert, caretaker boss Eddie Niedzwiecki has made seven changes from that team - including a first Premier League start since April 2015 for former Manchester City midfielder Stephen Ireland.
"But obviously we are going to try (for a new deal)". Of course he's going to try to give him a contract that keeps him here for much longer than that option that of course we are going to execute.
"I honestly believe Mkhitaryan is one of the best players in the Premier League, his confidence is just shot at United. I don't negotiate with players, I don't discuss numbers in contracts, I just say what is obvious, and any of you could say the same, that he is to keep".
When questioned on whether or not talks over an extension with De Gea were ongoing, the Portuguese manager replied: "I don't know".
"I think every player has a price. The situation is not completely decided one way or the other, so I left him at home".