Louis van Gaal accepted that David De Gea may want to leave Manchester United as he contemplated a problematic situation that he described as "not favourable" for anyone.
De Gea is a target for Real Madrid but United have insisted they would only sell the 24-year-old for a world-record fee for a goalkeeper, topping the £32.6 million Juventus paid for Gianluigi Buffon in 2001.
Real are yet to bid for De Gea and have further frustrated United by declining a €40 million offer for centre-back Sergio Ramos, Van Gaal's main defensive target.
United are willing to hold De Gea to the last year of his contract, although they run the risk of losing him on a free transfer next summer.
And Van Gaal said: "We have a situation that is not favourable for David De Gea, but neither for us and neither for the club [Real Madrid] that maybe he wants to go."
Real have allowed their long-term first-choice goalkeeper Iker Casillas to join Porto this summer but have brought in Kiko Casilla and given Keylor Navas the No. 1 shirt, hinting that they do not expect a deal for De Gea this year.
De Gea made his second appearance on United's preseason tour of America as they lost 2-0 to Paris Saint-Germain in Chicago on Wednesday.
And after Luke Shaw put the French champions ahead with an own goal, Van Gaal felt De Gea was to blame as Zlatan Ibrahimovic doubled the lead.
"I cannot say he [De Gea] did not make a mistake," Van Gaal added. "But everybody can makes mistakes and when a goalkeeper makes a mistake it is mostly a goal and that's the difference.