The highly-rated Benzema has been linked with Manchester United for the past six months, but the News of the World claim that the striker is now subject of interest from Arsene Wenger.
Should the future of £25m Togo striker Adebayor be decided in the next few weeks, Arsenal will be keen to bolster their strikeforce and a £30m bid for Benzema could be accepted.
The player has said that he would prefer another season at Lyon to make sure he cements a place in the France side for the World Cup. But the club's owners have hinted that a bid of more than £30m would turn their heads and Benzema is also believed to favour a move to the Emirates over Old Trafford.
Lyon president Jean-Michel Aulas' said last week that despite Benzema's apparent desire to stay at Stade Gerland, a sizeable offer could lead to him leaving.
"Karim has said that he wants to stay another year at Lyon," Aulas told L'Equipe. "But I think that Kaka or Ronaldo maybe imagined remaining with their respective clubs.
"There is a tsunami called Real Madrid which provokes reactions at Chelsea, Manchester City and Manchester United.
"So it is very complicated to say that he is non-transferable. It's obvious we want to keep him. There is more chance he'll be at Lyon next season than that he won't be.
"I won't hide from you the fact that he has been approached. For the moment, I managed to convince them not to go further."
Benzema has come through the ranks at Lyon and burst onto the scene in the 2007-08 season with 31 goals in 51 games, a streak that saw him named Ligue 1 player of the year as well as top the league's scoring charts.