The Daily Star says the 50-year-old has not agreed to go back to Stamford Bridge yet, because he does not want to be disrespectful to Real Madrid, who he hopes will win him a third Champions League following success with Porto and Inter.
He also is not keen on taking charge at Stamford Bridge if the Blues do not qualify for the Champions League.
Mourinho is also believed to have a list of demands that include getting rid of chief executive Ron Gourlay and technical director Michael Emenalo.
He has a list of transfer targets, which he will want assurances over.
But a comeback is looking increasingly likely, as his relationship with billionaire Abramovich has been restored, with the pair in regular contact.
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