Liverpool are asking for offers in excess of £60m for the 27-year-old, and Tottenham are understood to be prepared to meet that valuation as talks progress.
Gakpo's representatives have already agreed terms in principle with Spurs and have since made his position clear directly to Liverpool's hierarchy, with the forward telling the club he does not see his long-term future at Anfield.
The move comes as Liverpool continue reshaping their attack following Mohamed Salah's departure at the end of last season and the arrival of Andoni Iraola as manager in place of Arne Slot.
Rio Ngumoha's emergence on the left has pushed Gakpo down the pecking order, while Alexander Isak leads the line through the middle and Hugo Ekitike will return to full fitness at some point this season, leaving the Dutchman increasingly short of guaranteed game time.
Liverpool's primary transfer focus remains a move for Bradley Barcola, PSG's forward, and a Gakpo departure would help fund that pursuit, along with any move for Barcola's teammate Ibrahim Mbaye, who has also been on Liverpool's radar. PSG's move to sign Ajax winger Mika Godts for around €55m has been read in some quarters as a sign the French club are already planning for life without Barcola.
Gakpo has made 180 appearances for Liverpool since joining from PSV Eindhoven in January 2023, scoring 50 goals and adding 23 assists, and played a role in the club's 2024 Carabao Cup win and the Premier League title the following season, when his ten league goals were a career best. Tottenham's interest has been consistent throughout the summer as Roberto De Zerbi continues his own overhaul of the squad, with Gakpo seen as a versatile addition to the club's forward options.
Spurs have already been among the most active clubs in the market this window, with significant outlay on Sandro Tonali and Matheus Fernandes among others, and view Gakpo as the missing piece to complete their attacking rebuild.
With just over two weeks remaining before the transfer window closes, Liverpool face a tight timeline to both sanction Gakpo's exit and complete a replacement, whether that ends up being Barcola, Mbaye, or another attacking option altogether.