Minamino was sent out on loan to Southampton during the 2020-21 season to get more game time and experience.
He was not that crucial to Saints scoring 2 goals, although there was no option to buy in his deal, he returned to Liverpool.
The arrival of more attacking options such as Diogo Jota and Luis Diaz made Minamino's chances slimmer and now even slimmer with the arrival of Nunez Darwin.
He has taken his leave with a €15m plus €3m in add-ons deal with Monaco.
Minamino is already 27 and would need to play at the top level if he wants to leave his name etched in football.
Monaco finished 3rd in the Ligue 1 last season and are poised to participate in the UEFA Champions League -- a factor that could have attracted Minamino.