Olympique Lyon star Moussa Dembele is on Everton's shortlist.
Dembele will be out of contract and available for free at the end of the season but Everton could move beforehand to get ahead of the competition.
Lyon may also be attracted to the proposition of recouping a transfer fee for a player who would not bank them anything in a few months' time.
Dembele, 26, has scored twice in six Ligue 1 starts this campaign.
Atalanta striker Duvan Zapata is another under consideration by the Toffees.