The 34-year-old's contract is unlikely to be renewed by Les Gones, meaning that he will become a free agent this summer.
Malbranque told L'Equipe: "For now, I have had no meeting to talk about a prolongation, so it will be difficult. I don't think there will be any continuation with Lyon.
"My first wish is to go on playing. I still have desire. Going on here, why not, if the club wants me to stay?
"I have some contacts in Premier League, but leaving again is not my priority now. It would rather be staying in Ligue 1."
Malbranque has made 50 league appearances for Lyon since signing from Saint-Etienne in August 2012.