The attacker has attracted interest from a number of clubs this summer, with Liverpool prepared to cash in for the right price.
Minamino now looks set to end his association with the Reds, with Monaco having found an agreement on a fee with the Merseyside giants.
Monaco will pay Liverpool a fee of €15m for Minamino, according to French outlet Foot Mercato, and the sum will be paid over five instalments.
For Liverpool, offloading Minamino will bring in money to help offset the cash splashed to sign Darwin Nunez from Benfica earlier this month.
The Reds are also selling Sadio Mane to Bayern Munich, which will also bring in money for the club’s coffers.
Minamino, 27, clocked a total of 22 appearances for Liverpool over the course of last season and found the back of the net on ten occasions.
Now the attacker is poised to make the move to play in Ligue 1 with Monaco, who finished third last season and will go into the Champions League qualifiers later this summer.