Gakpo is set to sign for City after he gave the green light to the switch which will see Liverpool receive a £85M package for the winger this summer.
His departure comes as the Reds are set to announce the arrival of Paris Saint-Germain star Bradley Barcola later today, displacing the Dutchman from the side.
Barcola, arriving for around £120M is set to become the second most expensive signing in the club's history, behind Alexander Isak who cost the side £125M.
Speaking after the disappointing 2-2 draw with Nottingham Forest on Saturday, Van Dijk admitted that he wanted Gakpo to stay even if he wants more quality in his side after a difficult start.
"What do you think? He's a quality player. I think we should keep quality players," Van Dijk told reporters at Anfield when asked about the situation after the Forest draw.
"Let's see what the next few days bring. I want him to stay not only because he's a quality player but also because he's a friend of mine. He's very important for us.
"Adding quality to the squad always makes a difference," Van Dijk said. "Let's see what the next few days brings. After Tuesday we have to fight for everything with no regrets.”
Gakpo rustrated many Liverpool fans last season with his disappointing performances, but he has been in impressive form of late, scoring and assisting in the club’s opening games against Newcastle and Forest.
The 27 year old joined Liverpool from boyhood club PSV Eindhoven in January 2023 and has scored 33 goals in 91 Premier League appearances. He will now join rivals City who clash with the Reds in October.