Burnley value Michael Keane at £25m
Everton were reportedly interested in Keane in January and look set to step up their pursuit when the transfer window reopens in the summer.
Toffees manager Ronald Koeman is said to be in the market for a new centre-back to partner Ashley Williams.
Everton to beat Liverpool to Michael Keane in the summer
Everton's Merseyside rivals Liverpool are also in the running to sign the 24-year-old, but are way behind in the market at 11/4.
A BetStars spokesman said: "Few young defenders have been as impressive as Michael Keane this season and his performances have attracted the attention of several big Premier League clubs.
Players who have appeared for both Liverpool and Everton
Mon, February 27, 2017
Express Sport takes a look at some of the players who have crossed the Merseyside divide in one of the greatest rivalries in football
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Express Sport takes a look at some of the brave players who have crossed Stanley Park during their careers, playing for both Liverpool and Everton on Merseyside in recent history
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"Everton are the clear favourites to sign Keane at 11/10 followed by their Merseyside rivals Liverpool at 11/4.
"The chance to join Ronald Koeman’s improving side could prove an opportunity too good to ignore for Keane, so we expect to see him playing his football at Goodison Park next season."