The 27-year-old enjoyed an impressive 2020-21 campaign for Lyon, scoring 22 times and registering 12 assists in 40 appearances in all competitions.
The attacker's contract with the Ligue 1 side is due to expire at the end of June, though, and he will not be signing an extension, meaning that he is available on a free transfer this summer.
Barcelona have long been considered as the favourites for the Netherlands international, despite Juventus allegedly offering him a more lucrative contract.
Koeman has stopped short of officially confirming the forward's signature but has insisted that a deal to bring the Dutchman to the Catalan club is on the verge of being announced.
"The deal is almost done. Not signed yet, but it's almost completed. I wanted to sign him in January, but if it happens now, that's great. We know what we can do together," Koeman told Voetbal International.
Memphis, who is capable of playing in a number of attacking positions, will leave Lyon having scored 76 times and registered 55 assists in 178 appearances for the French outfit. body check tags ::