The Portuguese coach took charge of his final Real game on Saturday as the Spanish giants beat Osasuna 4-2.
Six years after an acrimonious departure from the west Londoners following a reported fall-out with billionaire Russian owner Roman Abramovich, Mourinho has long been rumoured to be on his way back.
And Sky Sports said he had arrived in the United Kingdom, less than 24 hours following his Real swansong.
Outgoing interim boss Rafael Benitez, who has now joined Napoli, had previously hinted that Mourinho was returning and although the Portuguese has refused to say so himself, it remains one of the worst kept secrets in football.
Mourinho won two league titles, an FA Cup and two League Cups during his previous stint in charge at Stamford Bridge, in just over three seasons, while he twice guided the club to the Champions League semi-finals.
In his three years at Real he won La Liga and the Spanish Cup once each while getting to the Champions League semi-finals every year, but failing to reach the title game.