Toffees boss Frank Lampard sees Cornet as a replacement for Rcharlison.
But a loan offer has been rejected by Burnley, says The Sun.
The proposal was to sign Cornet for the season and buy him only if Everton stay up.
Cornet, 25, is keen to stay in the Prem and Burnley would sell for £18million, although the Scousers will have to pay on a guaranteed basis.
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