De Gea is widely recognised as one of the best goalkeepers in the world.
And the Spaniard has had another impressive season for Manchester United despite keeping just three clean sheets.
United have been trying to tie De Gea down to a long-term deal for several months but talks have not resulted in an agreement.
De Gea’s current deal ends in the summer but United have the option to extend this by a further year.
But according to The Times, Juventus are keeping a close on eye on De Gea’s situation.
Mourinho was asked about De Gea’s contract issue and the United boss admitted he has doubts over whether a renewal will be sorted.
“I am not confident,” he told Sky Sports.
”I cannot find the word in English, but let’s see what happens.
“Only the club, David and his people can answer that.
“My comment is only that everyone knows how good he is, how important he is for Manchester United and, if the club want to be better than it is and not worse, obviously it would be very important to keep David.”
Wojciech Szczesny became Juventus’ No 1 stopper this season following Gianluigi Buffon’s transfer to PSG.
But a United insider told The Times: “De Gea played against his future club on Tuesday. Juve are an expert in intelligent deals.
“If United don’t sell him in the summer, Juventus will wait until the end of his contract.”
De Gea has been consistently linked with Real Madrid but a move to the Bernabeu appears unlikely after Thibaut Courtois joined in the summer.