The tight competition on the Liverpool front lines forced Minamino to leave for another team, actually Minamino is a good player, fast and agile but unfortunately he failed to get a main place in the Liverpool squad, his experience playing at Salburz used to be a reason for Monaco to sign him, Minamino arrival I think will make Monaco a better contender next season in Ligue 1, now the deal has been done for 12 million euros.
The tight competition to become Liverpool's first line of choice seems to be a reasonable reason why Liverpool should release their players to Monaco. But I think Liverpool are also trying to make the team's finances more balanced after Nunez was bought for a high price. The sale of Mane and Minamino will make financial conditions more stable but perhaps Liverpool will still be eyeing other players in the market.
I don't know much about the player, so I don't know how he actually performed at Liverpool. Regardless, Minamino is probably expected to be a fine signing for Monaco. There isn't much speculation and rumors about it, but it's done deal.