Gakpo, 23, has been in scintillating form at the start of the season, finding the net 13 times and providing 14 assists in 21 appearances across competitions.
The Dutch forward has the second-highest goal contributions in Europe behind Manchester City striker Erling Haaland who has 25 in 16 appearances.
PSV resisted interest in the Dutch winger throughout the summer and the winger remained at the Philips Arena.
However, they appear to be in need of funds and, therefore, would listen to offers for Gakpo around the £26 million mark.
Arsenal are a potential suitor for the Dutchman, as reports claim that the Gunners are looking to sign the winger in January.
He has four years remaining on his contract with PSV but as his stock continues to rise so too does interest in his services.
Gakpo showcased his talents against Arsenal in the Europa League on 27 October.
The Eredivisie side beat Mikel Arteta's side 2-0 in what was just the Gunners' second defeat of the season in all competitions.
Gakpo had two shots, made three key passes and made four crosses during the clash at the Philips Arena.
PSV manager Ruud van Nistelrooy was eager not to lose Gakpo in the summer and is aware that there is interest once again.
He told reporters prior to the win over Arteta's men (via Manchester Evening News):
"It's not only Premier League clubs after him. His quality and form over the last three or four months has been exceptional. His stats and goals draw the attention of big clubs in European football."
"He is 23 and is focusing on his career with us at club level and having a great World Cup. He wants to continue that. When the time comes he will make decisions."
Gakpo has made 157 appearances throughout his time at PSV, scoring 55 goals and providing 49 assists.
He has won the Eredivisie title once as well as the KNVB Cup.
Arsenal goalkeeper Aaron Ramsdale said that the Gunners' defeat to PSV was just a blip
Arsenal have now gone two games without a win for the first time this season following a 1-1 draw with Southampton on 23 October and the loss to PSV.
Despite this, Ramsdale doesn't believe the setback at the Philips Arena is a reality check for this side.
He was quoted as saying (via football.london):
"At the Southampton game we knew what went wrong and obviously we will look at what went wrong in this game in more depth. The manager is great giving us the detail we need to improve."
"So I don’t think it’s a reality check, I just think we need to go back to what we were doing, our basics better, than what we have shown in the past two games."
The Gunners sit top of the Premier League with nine wins, one draw and one defeat in 11 fixtures.
They also lead Group A in the Europa League, boasting a three point lead over second-placed PSV heading into the final matchday of the group stages.