The Toffees want to rescue the Belgium international from his Merseyside misery during the January transfer window.
Origi, 23, spent last campaign on loan at Wolfsburg but failed to secure a move away from Anfield during the summer.
Now he's been left in exile by Jurgen Klopp having been limited to just under-23 appearances for Liverpool this season.
The Reds slapped at £27million price-tag on his head before the beginning of the season but Borussia Dortmund baulked at the asking price.
They signed him in the summer of 2014 but has been limited to just 21 league starts in four years.
Reports in Turkey claim Everton boss Marco Silva is ready to bolster his attack by making a move.
Everton are in the market for a new front man with Cenk Tosun struggling to deliver.
Origi's goalscoring exploits are far from prolific, however, with the former Lille man failing to score more than eight goals in an entire league campaign.
If he does make the short switch across Stanley Park, he will become one a few players to do so.
Peter Beardsley made the move in 1991 alongside Gary Ablett and Don Hutchinshon.
Nick Barmby made the opposite switch when he left Everton for Liverpool in 2000.
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