An Anfield delegation met the PSV Eindhoven star for discussions along with his agent Kees Ploegsma.
Depay, 21, is understood to have been impressed by the vision outlined by Liverpool and the club will now approach Dutch champions PSV about striking a fee of around £20m for a player who has also interested Manchester United and PSG.
Liverpool manager Brendan Rodgers is keen to bolster his attacking options and Depay scored 21 goals as PSV won their first title in seven years.
It comes with injury-hit Daniel Sturridge's long-term future at the club plunged into doubt as Rodgers claimed he will buy a forward who can play at a "top level every week" for next season.
