The 23-year-old midfielder was part of Didier Deschamps' initial France squad for the World Cup in Brazil, but was ruled out prior to the tournament after pulling up with a groin injury in training.
Grenier made 28 Ligue 1 appearances for Lyon last season, scoring four times as the side finished fifth under the stewardship of Remi Garde.
"I have no problem with the club and have never missed a training session intentionally," he said.
"There is no controversy and my intention is to be back on the pitch and competing as soon as possible.
"To put things into context, I just want to make everyone understand that an individualised programme has been implemented in accordance with the medical staff and technical staff of the OL so I can return to 100 per cent of my abilities.
"This requires a suitable recovery period with a lot of individual work and muscle building that takes place indoors.
"This is why I am not present at certain meetings with the rest of the group."
