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.
If we look at Takumi Minamino statistics he very rarely got playing minutes last season because he failed to compete in the main squad, this is an option for Takumi to leave Liverpool this summer. Divock Origi is reported to have flown to Italy to undergo medical tests and he has officially joined AC Milan. There are still rumors that Liverpool will bring in another player this summer but I think they will be targeting Raphinha next.
On the other hand, their rivals Manchester City have reportedly managed to get Stefan Ortega who will become Manchester City second goalkeeper next season.
I think City and Liverpool are still very active in this transfer window. we can see the competition for the title race in the next season is tight.
But I must say when Minamino played it was nice to watch. He is a bit similar to Kagawa at Dortmund back at the time. Very dynamic and very good in changing gears, also in switching from defense to offense. I think it is no shame to not make it into the first squad in Liverpool. Even Firmino only was a substitute most of the time and it felt like every time he came onto the pitch he also scored, yet he wasn't first choice. I think in the right team Minamino could play a vital role. Imagine he keeps getting his minutes week after week. He hasn't had that situation yet in a top team, let' see what he might be able to turn into.