Levante are desperate to boost their attack for the second-half of the season and their search has led to their former star Kone.
TMW says the Spanish Liga club sounded out Everton about Kone's situation, but were informed the striker was unavailable.
The striker is recovering from a knee injury and isn't expected to be fully fit until the turn of the year.
Blues boss Roberto Martinez said last week: "I expect him to be fully fit by January and by that I mean match fit. He is going to be involved in 11-a-sides behind closed doors this week to build him up again and he will be fully fit in January. I've seen some players with it recover earlier and others take a lot longer to get back. But everyone does come back."
For the big stories and the banter follow us on Twitter: @tribalfootball