Bruce has 18 months remaining on his existing deal and has been touted as a possible successor to England boss Fabio Capello when he steps down after Euro 2012.
The Black Cats boss has hinted that he would be interested in leading his country, but has admitted that he would also like to discuss a new contract to stay with Sunderland.
Now it has emerged chairman Niall Quinn and owner Ellis Short, who have been impressed by Bruce's first 18 months under a three-year deal, have been in touch.
Bruce has led Sunderland into the top six of the Premier League and they are on course for a European place.
A victory over Aston Villa on Wednesday night, despite injuries to key players, has maintained their momentum and Sunderland are keen for Bruce's reign to head in to a fourth year.
Sunderland finished 14 points above the relegation zone in Bruce's first season in charge and he has helped Darren Bent and Jordan Henderson force their way into the England squad.