Chelsea boss Maurizio Sarri hopes to persuade the Belgium international to stay at Chelsea for at least another campaign, with talk of a switch to Real Madrid refusing to go away.
Sutton, a Premier League winner with Blackburn Rovers in 1995, insists that Sarri can forget about any silverware if Hazard does indeed depart.
"If they let Hazard go they're finished, they've got no chance this season," he told BT Sport. "[Thibaut] Courtois, that situation still seems to be up in the air and needs to be resolved, as do a lot of things."
Madrid have also been tipped to move for Courtois, while Willian is a rumoured target for Barcelona.