The Real Madrid coach is odds on favourite to take over from interim boss Rafa Benitez this summer, and is already said to be making plans to reshuffle the Stamford Bridge club's backroom staff.
Kean is available after resigning from his Ewood Park job last September, with Rovers third in the Championship, after failing to win the fans over following relegation from the Premier League in 2011/12.
The 45-year-old's reign was dogged by protests as he remained a deeply unpopular figure ever since his controversial appointment to succeed Sam Allardyce in December 2010.
However, he could now be offered a surprise route back to England's top-flight with Mourinho ready to appoint Kean as his assistant at Chelsea, to compliment his own team of loyal staff.
During his playing days Kean took in a spell in Portugal with Coimbra, and his ability to speak fluent Portuguese will be beneficial if he is to link-up with the 'Special One' at Stamford Bridge.
Surprisingly, it's not the first time that Kean has been on Chelsea's radar, as Luiz Felipe Scolari tried to bring the Scot to the club during his ill-fated spell in charge in 2008.