The 25-year-old's proposed move to Liverpool fell through last season, so he remained at Lyon for 2018/19.
Fekir scored nine goals in 29 league matches for the Ligue 1 outfit, watching from afar as Jurgen Klopp's side won their sixth European title.
A move to Merseyside may not be plausible this summer, but Fekir should consider his options away from Lyon, according to Genesio.
Speaking to French radio station RMC (via Goal.com), he said: "I think that he [Fekir] was very frustrated with his cancelled transfer to Liverpool at the beginning of the season.
"Nabil is coming to the end of a cycle in Lyon. He has experienced a lot of things here.
"I think that he needs a new challenge, to push his limits, and to be self-critical. Because we know we always need a personal challenge in a career, and to ask questions of ourselves."
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