Dembele joined Lyon last year from Celtic in a £19.7m move and has been impressive in his first season in France.
The 22-year-old bagged 20 goals in all competitions for the Ligue 1 outfit and this has attracted the attention of several of Europe’s big boys.
Lyon expect to receive bids for Dembele in the coming weeks, but are keen to hold onto the Frenchman as they expect to lose several key players.
Liverpool boss Jurgen Klopp is not desperate to sign a new forward but is looking to bring in some reinforcements to bolster the squad.
After their Champions League success against Tottenham in Madrid, they will be hoping to go one step better in the Premier League next season.
Despite finishing with 97 points, the third highest total in Premier League history, they still fell one point short of champions Manchester City.
With the club announcing that Daniel Sturridge will leave the club at the end of his current deal, Dembele would be seen as a good back up for the much-haled front three.
Should he leave Lyon, former club Celtic would be in for a cut in the deal after enforcing a 10 per cent sell-on clause in the deal when he was sold last year.
He bagged 51 goals in 94 games in all competitions in two years with the Scottish champions and is now valued at around £40m.
When asked about his future last month Dembele said: “I signed for five years with Lyon and I’m happy there but we’ll see what happens.
“I’m happy to stay with Lyon next season but we’ll see.”
Lyon’s sporting director Juninho insists Dembele will not be heading for the exit, this summer at least.
He said: “There will be only be three departures from the club this summer and they won’t be either Moussa Dembele or Memphis Depay.
“Moussa’s form has been a nice surprise for us this season. He’s very good technically and we want to build on that.
“We want to keep him and we will.”