Zenden left Marseille in the summer and has yet to find another club willing to pay his high wages.
The 33-year-old wants a move back to the Premier League and Portsmouth, Hull, Stoke and Blackburn have all been linked with him, but none are willing to match his wage request.
He has been invited by Steve Bruce to train with the Black Cats first-team squad during the international break.
Zenden's agent and father Pierre told Voetbal International: "Sunderland would like short term to strengthen the midfield and Boudewijn is a serious candidate.
"In the past months he has been very strict with himself and has worked six days per week to keep in shape.
"Sunderland know who he is and what he can do so he has no need to prove himself.
"They want to see him doing it and it just despends on medical tests."