The Mestalla outfit want the French trainer to take over from the out-of-contract Unai Emery at the end of the current season, according to sources close to Los Che
According to French radio station RMC, Los Che are keen to bring the former Juventus coach to the Mestalla, although a deal is yet to be negotiated between the two parties.
The report comes amid increasing pressure on the current incumbent of the Mestalla dugout, Unai Emery, whose contract runs out in the summer.
"We are interested in Didier Deschamps and his agent knows it. For next year, it is a reasonable possibility, but nothing is done," said a source close to Valencia.
Despite a tumultuous past few months at Marseille, Deschamps, 43, remains highly sought after and has been in the radar of Chelsea and Inter in recent weeks.
A move to the Liga giants would represent a step up for the former World Cup winner, whose notable achievements include guiding Monaco to the Champions League final in 2004 and winning the Ligue 1 title with OM in 2010.
Valencia are third in the Liga standings and are on track to secure automatic qualification for next season's Champions League.