Chelsea are believed to be in the market for a centre-back and may decide to move for Kone.
Chelsea could be tempted to join the race for Sunderland's Kone
Kone, who only joined the Black Cats in January, has seen his future become the subject of intense speculation in recent weeks, with reports suggesting Sunderland have already turned down a bid from the Merseysiders.
Everton are understood to have been impressed by the 27-year-old's performances during Sunderland's successful survival bid last term and have identified the former Lorient ace, as well as Swansea City captain Ashley Williams, as the perfect candidates to shore up a defence that has now lost John Stones.
Stones, who was previously linked with a move away from Goodison Park all summer, has finally completed a £47.5 million transfer to Manchester City, setting the wheels in motion for Toffees boss Ronald Koeman's transfer plans.
According to Foot Mercato, Everton will return with an improved bid for Kone, with an alleged five-year contract also reported to be on the table.
But while Everton are thought to be confident of completing a deal, they could yet face late competition from Chelsea, with the Daily Mail reporting that the Blues are already looking at alternative options to Napoli centre back Koulibaly, with the Serie A outfit seemingly reluctant to sell until they find a replacement.
But while Everton are thought to be confident of completing a deal, they could yet face late competition from Chelsea, with the
Kone is believed to be one of those potential options, alongside Benfica's Victor Lindelof.