It was agreed for the two parties to part company today after a meeting involving Maresca and Chelsea directors Behdad Eghbali, Lawrence Stewart and Paul Winstanley.
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Taking to social media, Cucurella posted: "Thank you for everything, mister, and to your staff. For the work and the trust from day one, and for the memories!
"Wishing you all the best in what comes next. Good luck, boss!"
Maresca leaves Chelsea after winning the Europa Conference League and Club World Cup titles, along with qualifying for the Champions League.