The French midfielder, who had been a top target for Newcastle, is wanted by several sides, including the Rossoneri, but is in no hurry to force an exit from Lyon
Grenier has been heavily linked with a move to the Premier League this year, with Arsenal credited with an interest before Newcastle United emerged as unlikely contenders for his signature.
The France international fuelled speculation that he wanted to quit Lyon when he missed a training session at the start of August, although he later insisted that talk of a "controversy" was blown out of proportion.
His representative, Frederic Guerra, has since claimed that Milan and two unnamed clubs are still keen on signing the 23-year-old, though he made it clear Grenier would not aim to force an exit from Stade Gerland.
"We will wait and see, as the transfer window is still open. There are three interested clubs, including Milan," he told Foot Mercato.
"I have been in contact with the Rossoneri, as he is a player who is of interest to them. In any case, Clement isn't determined to leave Lyon at all costs."
Grenier, who scored four times and provided five assists in Ligue 1 last season, has a contract until June 2016 with Lyon.