The Blues are engaged in talks with the former Manchester City assistant coach.
Per the BBC, the Italian is now the firm favorite for the job ahead of Roberto De Zerbi.
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Brentford's Thomas Frank is still in the mix, while Kieran McKenna has ruled himself out of the running.
The source adds that Leicester will not make it easy for Chelsea to take away their head coach.
The Foxes would be seeking 8 million to 10 million in compensation for Maresca.