The Leicester City manager has seen a 9m fee settled with Chelsea this week, having already held talks with Blues officials.
The Sun says Maresca impressed with the depth of knowledge he had for Chelsea's squad and also his insistence on his playing principles being respected.
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Winstanley and Stewart will now seek to settle on terms with the Italian over a three-year deal.
There is hope of Chelsea announcing Maresca's appointment in the next 48 hours.