Gakpo, 23, has been heavily linked with a move to the Premier League, with United, Arsenal, and Leeds among the clubs interested in the Netherlands international.
United manager Erik ten Hag held conversations with Gakpo over the summer before signing Antony in an £82 million deal from Ajax instead.
United is still interested in Gakpo, according to Foot Mercato, who has already scored twice for the Netherlands at the World Cup in Qatar.
According to reports, PSV has boosted their asking price for the winger to €60 million (£51.6 million) based on his current play.
United may look to accelerate their plans to sign Gakpo, with his asking price likely to rise even further if he continues to impress at the World Cup.
Gakpo has been in exceptional form for PSV this season with 13 goals and 17 assists from 24 matches.
Arsenal could rival United for the winger, who has been compared to former Gunners forwards Thierry Henry and Robin van Persie.
“Cody Gakpo is a very tall player with speed,” Dutch journalist Marcel van der Kraan said earlier this year.
“He has been voted national Dutch Player of the Year, by all the former Dutch internationals.
“Everyone in Eindhoven would be very sad to lose him. He’s the kind of guy who has speed with a good left foot and good skills.
“I have often referred to Thierry Henry and Robin van Persie, not maybe at the same value or quality yet, but they came into the Premier League as a left winger, then converted into a striker by Arsene Wenger and really did well.
“This boy is also being converted into a striker because he has had some great individual coaching from Manchester United legend, Ruud van Nistelrooy, who is now coaching PSV. And he was also his individual striker coach at the academy.”
“Cody Gakpo is a very tall player with speed,” Dutch journalist Marcel van der Kraan said earlier this year.
“He has been voted national Dutch Player of the Year, by all the former Dutch internationals.
“Everyone in Eindhoven would be very sad to lose him. He’s the kind of guy who has speed with a good left foot and good skills.
“I have often referred to Thierry Henry and Robin van Persie, not maybe at the same value or quality yet, but they came into the Premier League as a left winger, then converted into a striker by Arsene Wenger and really did well.
“This boy is also being converted into a striker because he has had some great individual coaching from Manchester United legend, Ruud van Nistelrooy, who is now coaching PSV. And he was also his individual striker coach at the academy.”
