The 27-year-old has again been in impressive form for his French club during the 2020-21 campaign, scoring 20 times and contributing nine assists in 35 appearances in all competitions.
Memphis's contract is due to expire at the end of June, though, and it appears unlikely that he will be signing a new deal with his Ligue 1 outfit.
Barca are believed to have come close to signing the Netherlands international last summer but were unable to get a deal over the line.
The Catalan outfit have retained an interest in the Dutchman, though, and according to OnzeTV3, Barca are in talks with Memphis over a switch to Camp Nou.
The report claims that the attacker is excited by the prospect of working under Ronald Koeman once again, having played for the now Barca boss during his time with the national side.
Memphis has scored 74 goals and registered 52 assists in 173 outings for Lyon.