The defender had reportedly asked to leave Sunderland this summer.
Manchester City's Sergio Aguero in action with Sunderland's Lamine Kone
The Black Cats defender is the subject of fierce speculation this summer after impressing in the second half of last season.
Everton are particularly keen on his signature, with HITC Sport understanding they made an official move for his signature three weeks ago.
Lamine Kone scores the second goal for Sunderland
So far a move has failed to materialise, although this week saw Sky Sports reporting he was asking for a move after the club failed to offer him a new deal.
That came courtesy of a statement he had posted, but Moyes says the defender is now claiming that has nothing to do with him.
“I expect him to stay. When I pulled him yesterday he knew nothing about his statement,” he told the Shield’s Gazette.
“I was disappointed with Sky for doing that without having it reconfirmed by the boy. His name was put to it. We told him we'll look to do a contract in September if that's what was said and we said we've had an offer from Everton as well.”
Sunderland's Lamine Kone in action with Crystal Palace's Jordon Mutch
It will now be interesting to see if Kone does remain at the Stadium of Light this summer.
It is not surprising that Everton are keen to sign him given the impressive performances he put in last season to help his side avoid relegation.
A move to Goodison Park could also be a tempting one with Ronald Koeman looking to lead them into an exciting new era, and whether that lure proves too strong remains to be seen.
West Brom's Saido Berahino in action with Sunderland's Lamine Kone