The Ligue 1 outfit have been linked for a move for the France international, who endured a torrid 2021-2022 campaign at Camp Nou rocked by injury.
A Europa League qualifying finish for Rennes has left Genesio seeking "sports guarantees" in regard to his transfer aims, and the World Cup winner - whom he previously coached at Lyon - would fit the bill.
"Sam is a player I know perfectly well," he said. "I trained him as a youth player and then in the Lyon first team. That creates a bond.
"You all know his history, his qualities [and] the setbacks he had last year. But he is still a high-level player, and we are interested in high-level players,"
Genesio touched on his desire to reinforce Rennes' squad too, adding that he needs an influx of fresh talent to replicate the club's 2021-2022 feats.
"I want to have sports guarantees," he said. "We just had a very good season. To continue, we need a quality group.
"I needed to have a lot of answers in the backbone of the team that we were going to be able to maintain and what we were able to do in terms of reinforcements."