The Toffees are determined to sign the midfielder permanently as his loan deal expires in the summer.
Everton remain as strong favourites to seal a permament move for the Portugal international at 2/1.
But the bookies have listed a handful of clubs to rival the Toffees for his signature in the summer, including their rivals Liverpool.
Betfair's Katie Baylis said: “Gomes has looked good at Everton on the loan deal from Barcelona and we make it 2/1 he will stay permanently at Goodison Park.
"Other clubs are likely to be looking closely as well though and we have it at 6/1 his next club will be Atletico Madrid, with Valencia at 8/1.
"Wolves are 8/1 while we have Liverpool at 10/1 to steal their neighbour’s talented recruit."
Betfair: Andre Gomes next club
Gomes has excelled since arriving in the Premier League and has become a key player for the Toffees after just six games.
He was also handed the man of the match award after the Merseyside derby at Anfield.
Gomes struggled during his two-year spell at the Nou Camp after signing Barca for £29million from Valenica.
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