The 27-year-old is impressed by the Blues and Reds, but is only willing to move abroad if a club shows enough desire for his signature.
Speculation this week had suggested Liverpool coach Rafael Benitez was set to swoop for the winger in a £10million deal, but even though there has been contact with the Reds, Malouda insists no such offer has been made.
"There has been no offer but it's true there has been direct contact," Malouda told L'Equipe newspaper.
"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)."
The former Chateauroux and Guingamp player, who this week earned his 29th cap for France in a 1-0 win over Georgia, admits both clubs offer a mouth-watering prospect.
"At Chelsea there is Didier Drogba, as well as everybody else," he continued. "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."