The France international, who is currently playing for Turkish side Trabzonspor, joined the Blues in 2007, but was released last year.
Football Direct News claims that West Ham United have watched him in action, but they face competition from the Baggies.
The report quotes a club source as saying that Malouda would add valuable experience to the squad.
"He (Malouda) is a quality player and would provide some great experience to the squad. If we stay up it looks like he's one who'll be high on our list of targets," the source said.
Boss Pepe Mel reportedly wants to bring in new players to replace the loan trio of Morgan Amalfitano, Scott Sinclair and Matej Vydra, who are set to return to their parent clubs at the end of the season.
Malouda has also played for Lyon and Guingamp.