The Daily Mail says it is tentative at this stage but contact has been made and Roman Abramovich is interested in enticing the Real Madrid manager back to London.
The Blues are still third in the Premier League table despite conceding more late goals and losing 3-2 at Newcastle.
The defeat allowed the chasing pack to close and the owner will not tolerate missing out on the Champions League. Whether an emotional reunion has the same pull for Mourinho is questionable and he will be influenced by the degree of control the Russian would be willing to afford him.
The influence of managers over recruitment and team-building has been eroded since he left Stamford Bridge in September 2007 and would be central to any negotiations.
The relationship between Abramovich and Mourinho has thawed since their acrimonious split, yet it would be a huge concession if the Chelsea owner were to let his next manager lead a team-building programme. Abramovich felt Mourinho had become too powerful when he was sacked.
The other major factor is Paris Saint-Germain, a project which appeals to Mourinho, although sources in Italy suggest Carlo Ancelotti will be granted at least one more year at the helm.