The former USA and Egypt manager has been mentioned as a possible replacement for the recently departed Dick Advocaat.
Stabaek chief executive Lars Hjorth says the club will not stand in Bob Bradley's way if Sunderland wants to offer him its manager position.
The American manager has worked wonders at the Norwegian side since he joined in January 2014, and has the small-budget side in second place in the league with just four matches to go.
Bradley's success has led to him being mentioned as a possible replacement for Dick Advocaat, who left his post as Sunderland manager last weekend.