Sergei stunner for Stoke
The accomplished defender could move in January after growing frustrated at his level of pay at The Britannia Stadium.
Southampton and Fulham have watched the 30-year-old in the past, although Sunderland's assistant manager Steve Cotterill was a confirmed admirer of the player during his time in charge of City.
Certainly, his English agent Billy Jennings believes his client could be playing in the top flight.
"Sergei loves Stoke City and was hoping the club would come up with something to keep him here," he told The Sentinel.
"He's not being greedy.
"He just wants recognition for what he has achieved for the club, and wants to secure his future because time is getting on for him.
"He feels he is being paid well below the market value for a player of his calibre, even taking into account today's depressed market.
"He is an international class defender and a left-sided centre back, which is a rarity in today's game, so there could be a lot of interest.
"Whatever happens, he will give his very best for Stoke City because the club has come to mean so much to him."
The former Dinamo Moscow defender still has 18 months to run on his present contract with Stoke.