The 21-year-old is one of the world's hottest properties at the moment, with Manchester United and Madrid reportedly among those in the hunt to sign him.
Spanish media today claimed that Benzema could soon put pen to paper on a deal at the Bernabeu in the next few days after Lyon accepted an increased offer of €35 million from Real.
However, Lyon's director of communications insists they have not agreed to sell the France forward.
"We certainly did receive an offer of a sum appreciably superior to the sum that has been mentioned, but nothing says that it comes from Real," communications director Olivier Blanc told L'Equipe. "There is no agreement with anyone."
United coach Sir Alex Ferguson has long been an admirer of Benzema and the Premier League team could decide to use some of the £80m earned from the sale of Cristiano Ronaldo to Madrid to tempt the striker to Old Trafford.
Benzema came through the ranks with the French club 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.
The last campaign was less impressive for both club and player, as Lyon ended the season without the Ligue 1 title for the first time in eight years, but Benzema nevertheless scored 23 goals in all competitions - an average of a goal every other game.