Bitton, 24, had a slow start to life with Celtic having arrived from Israeli club FC Ashdod in 2013, but has become a key player under Bhoys manager Ronny Deila.
A powerful midfielder with great composure in possession, Bitton has become a mainstay of the Celtic side - and some believe that he could become the latest Bhoys star to make the move to the Premier League.
Fraser Forster, Victor Wanyama and Virgil van Dijk have all left Celtic in order to join Southampton, and Bitton's performances now appear to be attracting interest.
The Shields Gazette note that Sunderland are still pursuing Bitton despite the Israeli international penning a new contract until 2020 just two weeks ago.
It's stated that, after that new deal, Celtic's asking price is now in the region of £10m - what they sold Van Dijk to Southampton for - and that could put Sunderland off.
With the added security of Bitton's new contract, Celtic are under no pressure to sell, and are right to ask for a large transfer fee for a player who is becoming increasingly important at Celtic Park, leaving Sunderland to potentially look elsewhere for new signings.