The Scot is rumoured to be interested in signing the left-back, who he brought to Goodison Park in 2007, but Kenwright has ruled out the sale of the 28-year-old and revealed that new boss Roberto Martinez is determined to retain his star players.
|16/1||Everton are 16/1 with William Hill to finish in the top four next season
"Most of our players, if not all of them, are under good, long contracts at the moment, and Roberto went through each of the players, talking on my sofa, saying what they could do.
"He is looking forward to getting all of them together and keeping hold of them. He rates them all.
"There has been no back and forward dialogue with Leighton about a new contract yet, but that will start. He knows we want him to stay."
Martinez is eager to work with his new left-back - and the rest of his players - and wants to build on top of what Moyes achieved during his 11-year stay at Everton.
"For me, Leighton has been the best left-back in the league for a few seasons now, and I'm really excited to work with him," said Martinez.
"This dressing room finished top six and it is one of the most impressive teams, who have developed a winning mentality - it is something we cannot afford to lose."