The Blues' current head coach, Mauricio Pochettino, is under pressure at Stamford Bridge following a poor debut season.
Ex-Chelsea midfielder, Emmanuel Petit, claimed it would be "interesting" to see Mourinho return and argued that he would give the team "character and personality".
Mourinho's close circle has refused to confirm if he would be interested in taking the job.
But they believe that "there is no appetite from Chelsea" to appoint him.
During his first stint at Chelsea, Mourinho clinched back-to-back Premier League titles, as well as the FA Cup and two League Cups.
He then delivered another Premier League title and League Cup trophy during his second spell.
