SoccerNews.nl reports that Spurs are hoping to persuade Gakpo to make the move to north London, with De Zerbi regarded as a coach who could maximise the Holland international's qualities in a wide attacking role.
Gakpo, 27, scored seven goals and added five assists in 36 Premier League appearances this season, starting 32 times.
He has been a consistent performer for Liverpool since joining from PSV Eindhoven for approximately £44m in January 2023 and is contracted at Anfield until the summer of 2030.
His future is uncertain. New manager Andoni Iraola is yet to make his intentions clear regarding each member of the squad, and Gakpo's long-term role under the Spaniard is not guaranteed.
Liverpool are simultaneously pursuing Yan Diomandé of RB Leipzig as a direct Mohamed Salah replacement, and the potential arrival of a high-profile winger could further limit Gakpo's starting opportunities.
Beyond Spurs, multiple clubs from England, Spain and Germany are understood to be monitoring his situation. Whether Gakpo himself is open to a departure, and whether Liverpool would be prepared to sell a contracted player who remains in Iraola's potential plans, are the two questions the coming weeks will need to answer.