According to Marca, Liverpool have been informed by a third party agent that he would consider departing Madrid at the end of the season – and Rodgers is intrigued by the prospect of being able to pair him with Luis Suarez.
However, Karim Benzema insists he plans to stay at Real Madrid despite being linked with a move away from the Bernabeu.
Real are thought to be preparing a new deal for Benzema as they look to ward off any interest in the France international.
Paris Saint Germain and Arsenal are thought to be monitoring Benzema’s situation at Real, but the former Lyon man says he is not looking to leave the Spanish capital.
“I am happy here. I only think of Real Madrid and I consider that this could be my big year,” Benzema told Marca.
Benzema came under fire from some Real fans last season, but the forward has won over his critics this term and he has thanked coach Zinedine Zidane for helping rebuild his confidence.
“For me it was very hard to hear cries from the grounds in the Bernabeu but I have matured and now the situation is different,” he added.
“The support from Zidane was key for my morale recovery.”
Real are battling for honours on three fronts and Benzema claims they are determined to try and win everything on offer.
“Our goal is to win the lot. We’ve already made the cup final and we’re well placed in the other competitions. There are some top teams left in the Champions League.”
Written by Steve Milne @stevenmilnelive