Louis van Gaal has asked Manchester United’s board to sanction David de Gea’s departure to Real Madrid, according to reports in Spain.

The goalkeeper has been linked heavily with a move to the La Liga club throughout the summer transfer window and the AS newspaper says that Van Gaal has tired of what has become a drawn-out saga, requesting that De Gea is moved on at the earliest opportunity.

The U-turn over De Gea – who has a year left on his contract at Old Trafford – is reported to have come after the 25-year-old performed poorly in a 2-0 defeat to Paris Saint-Germain on Wednesday, being involved in a mix-up with Phil Jones and Luke Shaw that resulted in the French side’s opening goal and subsequently being substituted at half-time.

After that match, the cracks in Van Gaal’s patience were visible. “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 [to],” said the United manager. Later, he added: “Everybody can make mistakes but when a goalkeeper makes a mistake it is mostly a goal and that’s the difference.”

Van Gaal is now believed to have pressed for a relaxation of the club’s stance on De Gea, which has involved a hard-line over any fee and a willingness to let the player’s contract run down if necessary. United are thought to be seeking £25m for De Gea, who was signed from Atlético Madrid in 2011, but Real may feel under little pressure to part with that kind of money this summer. Although the long-serving Iker Casillas departed during the summer, the Real manager Rafael Benítez can call upon Keylor Navas and Kiko Casilla and will be aware of De Gea’s availability on a free transfer a year from now.

The prospect of keeping De Gea for another season may be less appealing to United if Van Gaal expresses a view that his state of mind is disruptive to his squad. An improvement on last season’s fourth-place Premier League finish is expected this time around and there has been a positive sheen to the club’s transfer market performance this summer, with the arrivals of Memphis Depay, Bastian Schweinsteiger and Morgan Schneiderlin providing a sense that Van Gaal is stamping his identity on the side. Allowing any ambiguity to rumble towards the end of the transfer window, by which time United will be four games into their league campaign, could risk compromising the kind of start required for a title race.

De Gea is the second goalkeeper at Manchester United to face an uncertain future, with his compatriot Victor Valdes – signed by Van Gaal to provide competition in January – recently placed on the transfer list after Van Gaal claimed he had refused to play for the reserve team.

The Argentina international, Sergio Romero, joined on a three-year contract last week after an impressive Copa América. He is well known to Van Gaal from the pair’s time at AZ Alkmaar but was not a regular for Italian side Sampdoria last season and any sale of De Gea would force Van Gaal to consider whether Romero and the Dane Anders Lindegaard would constitute sufficient depth in their position this season.