The defender has been heavily linked with Everton.
Lamine Kone’s agent has told Sky Sports that his client will train with Sunderland this week and is available for selection for the weekend clash with Manchester City, amid strong links to Everton.
The defender was a big hit at the Stadium of Light last season after joining in the January transfer window.
He played a major role in plugging a previously leaky defence and helping them avoid relegation from the Premier League under the guidance of Sam Allardyce.
Lamine Kone scores the second goal for Sunderland
That form has sparked interest from Everton, who HITC Sport understands have already seen offers of £16 million and £18 million rejected.
His agent has refused to comment on the speculation though, instead insisting his client will be available for the Black Cats to select this weekend as the Premier League season gets underway.
"Lamine will train with Sunderland tomorrow morning and is available for selection for Saturday. In the meantime Lamine still awaits the offer of a new contract from the club,” he told Sky Sports.
Sunderland's Lamine Kone in action with Crystal Palace's Jordon Mutch
It now remains to be seen if Kone is still a Sunderland player by this weekend, with Everton looking extremely keen on his signature.
They are now in desperate need of another centre back after selling John Stones to Manchester City and it appears they are especially keen on Kone.
With the looking likely to make an improved offer, it will be interesting to see how long Sunderland hold out before taking the big profit currently on offer.
Sunderland manager David Moyes