The 19-year-old is yet to score in 13 appearances since joining in an initial £27.5million deal from Juventus in August.
He was dropped from a matchday squad for disciplinary reasons last month and has been urged to return to Italy by his dad, Biorou Jean.
Italian outlet Gazzetta dello Sport claim Serie A club Bologna are keen to take the forward on loan in January.
Last month, former Everton boss Marco Silva, who was in charge when Kean arrived at Goodison Park, backed the youngster to come good in England.
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He said: “Moise has all the support here. He doesn’t need to find anything more for his career.
“We bought him. We really believe in him. He has all the support from the club, myself, from his teammates in order to keep adapting to the Premier League.
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