The Toffees are looking at a number of options to hand Frank Lampard extra attacking firepower to try to drag the side out of the Premier League relegation zone.
A number of players are under consideration at Goodison Park and, according to French outlet Foot Mercato, Lyon hitman Dembele is one of them.
Dembele is approaching the end of his contract with Lyon and Everton have been looking to wait until the summer to sign him as a free agent.
Given their fight for survival though, Everton are considering bringing forward those plans.
Everton are looking at making an offer to Lyon to sign Dembele this month to take him to Goodison Park now.
Dembele has made 14 appearances in Ligue 1 for Lyon so far this season, hitting the back of the net twice, and is not a starter under coach Laurent Blanc.
He has limited experience of Premier League football, but did star in Scotland at Celtic, where he scored 51 goals in 94 games.
