"At the moment, we have not had many enquiries," The Sunderland Echo quotes Aulas as saying about Grenier.
"We had an offer from Sunderland, I do not know what the status of that is. There has also been an enquiry from Italy. He has his own destiny in his hands."
Grenier has been on the books of Lyon his entire professional career so far and has a contract with the French club until June 2018, according to Transfermarkt.co.uk.
The France international attacking midfielder has been put on Lyon’s transfer list after struggling wth injuries for two years, according to The Sunderland Echo.
The 25-year-old scored two goals and created 18 chances in 18 Ligue 1 appearances for Lyon last season.
During the 2014-15 campaign, the Frenchman scored one goal and created 12 chances in six league matches.
Back in 2013-14, Grenier created 16 chances in seven Ligue 1 games for Lyon, while in 2012-13, the attacking midfielder scored three goals and created 19 chances in 14 league matches.
The fact that Grenier has (reportedly) been transfer-listed by Lyon means that Sunderland would be able to get him on the cheap.
It is hard to say whether the Frenchman would be a success in the Premier League, especially as he has not played too much first-team football in recent years.