Del Piero, 37, will be a free agent at the end of the season following revelations from Juventus that they would not be renewing his contract.
The former Italian international has been linked with moves to Paris Saint-Germain and a host of American clubs, but it now appears that Marseille have entered the race for his signature.
"I have respect for what Alessandro has done in his career," Deschamps told Rai Sport.
"He's a champion whom I've had the good fortune to have as a teammate and then a player.
"If he chose to come to Marseille, I would welcome him with open arms."
Del Piero has scored one goal in 16 outings this season.