Juventus are masters of the transfer market and are a tempting proposition for De Gea.
The goalkeeper has been the club’s player of the year in four of the last five seasons.
De Gea is an integral part of the club and losing him at the peak of his career would be a catastrophe.
Since arriving from Atletico Madrid for £18.9m, the Spaniard has developed into one of the world’s finest stoppers.
But it’s feared that De Gea has decided to call time on his Old Trafford career after eight seasons.
“De Gea played against his future club on Tuesday,” an Old Trafford source admitted to The Sun.
“Juve are experts in intelligent deals.
“If United don’t sell him in the summer, Juventus will wait until the end of his contract.”
Juventus have stung Manchester United in the transfer market before.
Paul Pogba came through the youth ranks at United before being lured to Serie A by The Old Lady.
Jose Mourinho convinced Red Devils’ chiefs to shell out £89m to bring him back to the club four years later.
Juve boss Max Allegri now has designs on repeating the trick by capturing De Gea on a free transfer.
Should they lose the 27-year-old goalkeeper, United would be looking at a huge figure to recruit a replacement of similar quality.
Atletico Madrid’s current No.1 Jan Oblak would be the ideal candidate although his release clause stands at £89m.
Juventus’s 1-0 win at Old Trafford on Tuesday left United battling with Valencia for second place in their Champions League group.
Mourinho’s men return to Premier League action when they welcome Everton to the Theatre of Dreams on Sunday (4pm).
United may be forced into a cut-price sale next summer with the risk of losing him for free 12 months later.
De Gea had been linked heavily with Real Madrid but that appears to be dead in the water after they signed Chelsea keeper Thibaut Courtois.