The winger has impressed at Goodison Park this season.
On-loan duo Arnaut Danjuma and Harrison will return to Villarreal and Leeds respectively.
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However, Everton will continue to hold talks with Leeds regarding Harrison.
Thelwell told the club's website: We thank Arnaut and Jack for their roles in the progress made by our men's team this season under Sean (Dyche) and his coaching staff.
"We will continue discussions with Leeds about Jack's future in the coming weeks."