The 35-year-old former England international was told by the Old Trafford club he would not be offered a new contract after their final game of the Barclays Premier League season.
Ferdinand won six Premier League titles, the Champions League in 2008 and three League Cups under Sir Alex Ferguson following his move from Leeds United for a then-British record transfer fee of £30million in 2002.
He has admitted that he is undecided about his future, and has been linked with a number of clubs, including Arsenal, LA Galaxy in Major League Soccer, as well as Turkish sides Besiktas and Galatasaray.
Bruce's club are another to have been mooted as a possible destination for Ferdinand, and speaking after Hull's defeat to Arsenal in the FA Cup final, the Tigers' manager said he may make contact with Ferdinand soon.
"We've cast an eye over a few things, I haven't looked into that yet," he said. "Rio has been a wonderful player... who knows?
"If he fancies a game, once we've got over the weekend, then I'll see if we'll give him a call."