The 23-year-old was the subject of persistent interest from Manchester United during the summer, and the Red Devils were widely expected to welcome him to Old Trafford next month.
However, Liverpool unexpectedly hijacked a move for Gakpo, who is confirmed to be leaving PSV in a club-record deal, believed to be worth an initial £37m with a potential £13m in add-ons.
Here, Sports Mole looks at which shirt numbers are available to Gakpo as he gears up for life in the Premier League.
For the past two seasons, Gakpo has donned the number 11 jersey for PSV while scoring and assisting goals for fun, but the Netherlands international can laugh off any chances of taking that iconic shirt at Liverpool next month.
Indeed, Mohamed Salah has worn the Liverpool '11' since arriving at Anfield in the 2017-18 campaign and is unlikely to relinquish that number, but Jurgen Klopp's side are currently without a number 10.
Sadio Mane sported that number for four seasons before leaving for Bayern Munich in the summer, and no member of Liverpool's existing squad was bestowed with the '10' - which has also been worn by Philippe Coutinho, Michael Owen and John Barnes - following his sale.
It is not difficult to envisage Gakpo being handed the '10' for the remainder of the 2022-23 season, although he currently wears '8' for the Netherlands, a number currently taken by Naby Keita at Liverpool.
Keita could very well be leaving Liverpool on a free transfer at the end of the season, which would free up the '8' for Gakpo to use, while Roberto Firmino's '9' could also become available if the Brazilian does not extend his contract beyond the summer.
While first emerging onto the scene at PSV, Gakpo boasted the number 19 jersey, although that shirt is currently in Harvey Elliott's possession at Liverpool and should not change hands so soon.
In terms of other vacant numbers, the '12' at Anfield does not have an occupier since Joe Gomez was upgraded to the '2' in the summer, while the number 16 shirt is also free after Marko Grujic finally completed his permanent exit this summer.
However, the '12' and '16' Liverpool jerseys have typically been worn by defenders in recent times, but the vacant 18, 24, 30 and 31 shirts have been sported by some notable and underwhelming attacking names down the years.
The '31' has been untouched since Raheem Sterling's exit in 2015, while Takumi Minamino's summer transfer to Monaco freed up the '18' for a new owner. As much as Gakpo would desire the iconic '10', this year's January arrival Luis Diaz took the '23' after leaving Porto, so the PSV man may have to prove himself in Anfield red before working his way into the lower numbers.