The Frenchman has repeatedly stated his desire to move to the Premier League and Liverpool had been thought to be favourites for his signature.
However, it now appears Blues boss Jose Mourinho will make his fourth signing of the summer with Lassana Diarra moving in the opposite direction, possibly on loan, according to French radio station RMC.
Malouda said recently: "Liverpool and Chelsea have shown their interest. I don't know how it's going to end but in my head I'm going to leave (Lyon)."
He added: "At Chelsea there is Didier Drogba, as well as everybody else, but then at Liverpool, they have such a good coach and the team has played in two Champions League finals in three years.
"The most important thing for me will be the desire shown by the club. To go and play abroad, you really need to be wanted."
The fee is likely to be in the region of £17million for the 27 year-old international and if he signs he will follow free transfer captures Steve Sidwell, Claudio Pizarro and Tal Ben Haim in moving to the Bridge this summer.
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