Hearts are on the hunt for their first "football manager" since George Burley left the club in 2005.
Santini, who managed France at Euro 2004 before an ill-fated spell at Tottenham, has thrown his hat into the ring to take over the Tynecastle hot-seat.
Santini's Scottish representative Alex McLaughlin, who has worked with Hearts in the past, told the Daily Express: "I have put Jacques Santini's name forward to Hearts and I am waiting to hear back from them.
"Hearts are on the lookout for a top-drawer coach with experience in the British game and, for me, Jacques Santini ticks all their boxes.
"He has shown throughout his managerial career that he is a top-level coach and I would be surprised if Hearts didn't want to follow things up."
Santini left Spurs after just 13 games in charge in 2004 following a reported bust-up with director of football Frank Arnesen, but previously led Lyon to their first ever Ligue 1 title in 2002 and his work there led to him being appointed as France coach in the same year.
Despite winning 15 of his first 17 games in charge, he was not offered a new deal by the French Football Federation following a shock exit to Greece at Euro 2004.
Most recently, in 2006, he coached Auxerre, but was sacked after failing to qualify for Europe.