The Frenchman, who arrived on Merseyside from Portsmouth in 2009, is out of contract with the Toffees next summer.
Reports suggest Everton have offered the 33-year-old a new one-year deal, but he is holding out for a further year.
"We have started talks and I am encouraged by that," Distin told the Daily Express.
"It's going well, quite positive. The club has one of the best atmospheres in the dressing room."
Distin is entitled to sign a pre-contract agreement with a foreign club in January.
The stopper has established himself as a key member of David Moyes' squad since his £5million arrival and has started their five opening Premier League games this season.