The 31-year-old centre-back has made more than 70 league appearances since arriving from Manchester City in 2007, helping the south coast club achieve FA Cup glory a year later.
However, the Frenchman has just 12 month's remaining on his current contract, leading to speculation linking him with a move away from Fratton Park.
Villa, Liverpool and Sunderland have all been tipped to sign the stopper, with Everton also reportedly keen following the sale of Joleon Lescott to Manchester City.
Distin has only recently taken on the captain’s armband at Pompey following the summer departure of Sol Campbell, and took no part in the club's midweek Carling Cup win over Hereford due to injury.
And club chief Storrie has now conceded that Distin is desperate to move on, with the Toffees making an offer to try and take him to Goodison Park.
"Sylvain told us that he wanted to go and we have had a bid from Everton," he told the Portsmouth News.
"I expect him to go, although I'm not quite sure how soon.
"It is disappointing because we would have liked to have kept him.
"We even offered him a new contract. We had previously turned down approaches, too. But Sylvain wants to go."
