The 23-year-old attacking midfielder has made 87 appearances for the Ligue 1 side since graduating from the club’s academy in 2009, but understands financial reasons could spell an end to his time at the Stade Gerland.
Newcastle boss Alan Pardew attempted to sign Grenier during the January transfer window, but the club’s £8million bid was rejected by Lyon.
Despite the rejection earlier in the year, Grenier remains open to a move away from Lyon, but insists the deal must suit his current club.
“You never know what can happen,” the Evening Chronicle quoted him as saying. “I think first I have to prepare myself.
“I’m at Lyon, but I know that economic reasons may change that. If it happens then it will, in any case, the decision must be made together.
“If it allows me to take the next step and it helps the club….For now, there is no news and I move forward with the club.”