The French giants are prepared to give the France international a way out of Stamford Bridge after he was deemed surplus to requirements by Blues' boss Roberto Di Matteo
The 32-year-old has fallen down the pecking order at the club to the point where he is now no longer part of manager Roberto Di Matteo's first-team plans.
The France international was left out of Chelsea's squad for the Champions League and claimed he has been forced to train with the reserves.
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Malouda joined the current European champions from Lyon in 2007, and their president, Jean-Michel Aulas, says he would welcome the midfielder's return to the Stade Gerland.
"Our door is always open to former players," Aulas told reporters.
"Malouda has been in contact with our coaching team very recently."
The Lyon president also left the door open for Jeremy Toulalan to return to the club from financially unstable Spanish side Malaga.
"We've also spoken with Jeremy Toulalan who has been having problems at Malaga."