The current Blues boss is expected to leave Stamford Bridge this summer after a disastrous Premier League title defence.
And The Sun say Juventus chief Allegri is keen to takeover in west London.
Allegri wants to test himself against the likes of Pep Guardiola, Jose Mourinho, Jurgen Klopp and Mauricio Pochettino.
The Sun add that Allegri has started learning English ahead of a possible move.
Real Madrid want to re-sign Alvaro Morata at the end of the season.
The Spain international quit the Bernabeu last summer in favour of a move to Chelsea but the striker has struggled to impress.
And Don Balon say Real are readying a bid for their former hitman.
They also reckon Abramovich is willing to take a loss on the Spaniard and sell him after one season.
The Daily Telegraph reckon Eden Hazard and Thibaut Courtois could join Real Madrid with the Blues willing to cash in on the star duo.
While Cesc Fabregas, Pedro Rodriguez, Gary Cahill, David Luiz and Olivier Giroud will only have one year remaining on their current contracts and could also leave Stamford Bridge.
Michy Batshuayi and Kurt Zouma could also be axed at the end of the season.
The Telegraph say the Blues will make a decision on the loan stars this summer once their managerial crisis is resolved.
A Freelance Journalist, Entrepreneur and Philanthropist. Editor-in-Chief of www.233times.com. A contributory writer for Ghanaian Chronicle Newspaper. An alumnus of Adisadel College where he read General Arts. He holds first degree in Bachelor of Arts from the University of Ghana; Political Science (major) and History (minor). He has also pursued MSc Corporate Social Responsibility (CSR) and Energy with Public Relations (PR) at the Robert Gordon University in the United Kingdom. His mentors are Rupert Murdoch, Warren Buffet, Sam Jonah, Kwaku Sakyi Addo and Piers Morganview all posts by: Nana Kwesi Coomson
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