Zenden has spent the last two days training with the Sunderland squad as he attempts to secure a return to English football.
The 33-year-old has played for Liverpool and Marseille since leaving Middlesbrough in July 2005, but is currently a free agent.
He was offered an opportunity to prove his fitness on Wearside after talks with Portsmouth broke down, and his father and agent, Pierre, is confident a short-term deal can be struck.
Sunderland want to examine Boudewijns physical state over the next two weeks, said Zenden Snr. 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.
Sunderland 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.
Steve Bruces interest in Zenden suggests he has no confidence in Daryl Murphy, the only player in his current squad who can realistically provide left-sided cover to Kieran Richardson and Andy Reid.
Zendens wage demands were a sticking point in his discussions with Portsmouth, but with the end of his playing career drawing near, the former Holland international, who has also played for PSV Eindhoven, Barcelona and Chelsea, is understood to be willing to accept a lower offer in order to secure a return to the North-East.
Bolo has joined us for a while and will train at the Academy for a few weeks as he looks for a new club, confirmed Bruce.
He clearly has a first-class pedigree as a player so its great to have him here.
Meanwhile, Lee Cattermole has withdrawn from the England Under-21s squad for this weeks European Championships qualifier with Macedonia.
Cattermole reported for duty with the rest of the squad at the start of the week, but the heel injury he sustained during the last international break has forced him to make an early return to Wearside.
The midfielder aggravated the long-standing problem in last weekends 2-2 draw at Manchester United, and will now receive treatment at the Academy of Light.
Sunderland officials are confident he will be able to take part in the clubs next Premier League outing, a home game against Liverpool on October 17.