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Gakpo, 23, had been heavily linked with a January move to Old Trafford after an impressive World Cup for Netherlands, scoring three goals en route to the quarter-finals.
But Liverpool have snuck under the radar to acquire the Dutchman's services in a deal believed to be worth as much as £45m.
PSV say Gakpo will travel to England to complete the deal, adding that it would be a record transfer for them.
Liverpool have made a move with established forwards Luis Diaz and Diogo Jota facing lengthy spells on the sidelines.
But who is he and what might he bring to the team's attacking play? Read on to find out more.
Who does Cody Gakpo play for?
Gakpo plays for PSV Eindhoven, having come through their academy. He initially turned out for Jong PSV, before making his debut for the first team in February 2018.
Success didn't come instantly for Gakpo though and he was forced to drop down to PSV's second-string side before returning to the Eredivisie and scoring for the first time in the top flight against Go Ahead Eagles in February 2019.
Gakpo made significant progress in 2019/20, but it was last season, following the transfer of Donyell Malen to Borussia Dortmund, when the Dutchman really puffed his chest out, bagging 21 times in all competitions for PSV.
Gakpo has pushed on even further this term, with 12 goals in 23 games across all competitions at club level. However, it is his assists tally that is the standout figure - 16 over the same period.
What is Cody Gakpo's style of play?
Gakpo is often located on the left of an attacking three behind Luuk de Jong, but can also do damage on the left of a front three, as he has had to do on several occasions this season, and has the game to play up top on his own if required.
Gakpo's finishing has stepped up a notch in the last year or so - an improvement no doubt accelerated by the arrival of new head coach Ruud van Nistelrooy in the summer - but the 23-year-old has previously cited Van Nistelrooy's fellow Premier League legend Thierry Henry as a player he looked up to growing up.
There are certainly parallels between the two, who both glided across the pitch, could beat the press with ridiculous ease and had the ability to terrorise defences at will and finish unerringly in a variety of ways and from a range of distances.
What makes Gakpo particularly attractive to any potential Premier League bidders however is his supreme passing and crossing ability, with the versatility to knock the ball around quickly as well as possessing the vision to slip in a team-mate for a strike on goal.
Cody Gakpo's World Cup performances
Gakpo went into the World Cup as one of the tournament's most talked-about young players and he delivered in the group stage, kicking off his campaign with a well timed run and glancing header to put the Netherlands ahead against Senegal on 84 minutes in a 2-0 win.
He doubled his tally in Qatar five minutes into the game against Ecuador when he controlled Davy Klaassen's lay-off, took two touches to advance and then lashed home from the edge of the box to give opposition goalkeeper Hernan Galindez absolutely no chance. However, the South Americans equalised through Enner Valencia and the Oranje were unable to find a winner.
Gakpo's skillset was most evident in the goal he scored in the final group game against the hosts though, producing a lovely give-and-go with Klaassen before driving forward and finding the bottom corner with aplomb.
The last-16 clash against the USA was the first game in which Gakpo failed to score, but he did lots of good ball carrying and linking up with Memphis Depay and Denzel Dumfries, including supplying the pass that allowed Dumfries to cut back perfectly for Depay's opener.
However, Louis van Gaal's men looked noticeably more disjointed in their quarter-final against Argentina, and although Gakpo continued to work tirelessly, his deliveries wasn't quite finding their mark and he was prevented from driving into central areas where he could get shots off, eventually being replaced on 112 minutes as the eventual winners prevailed on penalties.
Which clubs were interested in Cody Gakpo?
When asked by Dutch outlet NOS which clubs he would like to join, Gakpo expressed a desire to join one of five teams: "Real Madrid, Barcelona, Manchester United, Manchester City and Liverpool.
"It would be an honour to play there, but I also have to see what kind of team I can best achieve my goals [in]."
Ruud van Nistelrooy seems resigned to the prospect of losing his protege, recently telling Voetbal International: "If I have the choice, I prefer the summer [for the transfer to happen], but it can also be now. You just know there comes a time when you can't say no."
PSV Eindhoven director of football Marcel Brands, formerly in charge of transfers at Everton, also said on the possibility of Gakpo leaving: "You have to be realistic.
"When you talk about Cody Gakpo and the price tag, how many clubs are able to buy a player of that calibre? You are talking about maybe 10 or 12 clubs in Europe.
"It must be a record transfer for PSV anyway. Then you know in which direction it should go."
According to CBS' Ben Jacobs, PSV are looking for around £50m, comfortably eclipsing their current record sale Hirving Lozano, who joined Napoli in 2019 for around £40m.