The 34-year-old, who is in the final year of his contract, has been reported to be stalling on negotiations with the Premier League side in the hope of receiving a better deal.
Despite these suggestions, the former Portsmouth player has admitted that he is “happy” to accept the Merseyside club’s original offer.
"I read today in the newspaper that I was asking for a two-year contract. I am not sure where that has come from but it is completely untrue, and I would like to rectify that," the Liverpool Echo quotes Distin as saying.
"I am happy with one year. If Everton want to give me two then that is all good, but I am really happy with one."
Meanwhile, the Toffees are gearing up for the Merseyside derby against rivals Liverpool at Goodison Park this Saturday.