The Mirror says Mourinho, 50, is set to leave Real Madrid this summer after their Champions League exit.
The 'Special One' has already started planning for a tantalising second spell at Stamford Bridge.
He is interested in bringing in ex-Blackburn boss Kean to boost his coaching set-up.
Mourinho has his own loyal backroom staff but likes to have an assistant manager from the country he is working in.
He previously had Steve Clarke under him at the Blues but the Scot is now content as West Brom manager.
Kean, 45, is available after quitting relegated Rovers last September saying he was "forced to resign" despite the Championship club being third.