The Dutch winger, 33, will train with the Black Cats as he looks to impress a new club.
Zenden’s father, Pierre Zenden, hinted that he hoped Sunderland would be tempted to sign his son.
He said, “Boudewijn has, over the past few months, kept himself fit and trained six days a week.
“Sunderland are looking at a short-term way of strengthening their midfield and Boudewijn is a serious candidate. They know what he can do and what he is capable of so he does not have to prove himself.
“But they want to see him in action and submit him to some medical tests.”
Zenden was signed from Midlesbrough by Reds boss Rafa Benitez in the summer of 2005, making 23 appearances and scoring twice before Marseille signed him in 2007.