The Leicester City head coach is ready to accept the Blues' offer, as they settle on terms with the Foxes.
Todd Boehly and the Chelsea ownership group believe he is the ideal new manager.
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The Sun and other outlets believe that Chelsea have triggered the 9 million release clause in his contract.
Chelsea's co-Sporting Directors Paul Winstanley and Laurence Stewart will speak with him face to face in the coming day.
He has now pushed ahead of Roberto De Zerbi, Kieran McKenna, Thomas Frank and Thomas Tuchel to replace Mauricio Pochettino.