Ferdinand revealed on Monday he has played his last game for United but claimed he is "ready for a new challenge", opening up the possibility of extending his playing career at another club.
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"We've cast an eye on a few things. I haven't looked into [Ferdinand] yet, because the news only broke last night," Bruce said on Tuesday.
"Rio has been a wonderful player. Who knows? If he fancies a game... We've got Arsenal at Wembley on Saturday, so let me get over the weekend first, then I'll see if we'll give him a call."
Bruce has form when it comes to signing former United players, having recruited Wes Brown and John O'Shea during his time as manager of Sunderland.
Meanwhile, Bruce took the time to bemoan the sacking of Tim Sherwood at Tottenham, saying it reminded him of the way coaches are sacked in South America and other European countries.
"Looking at it from the outside, Tim's done a really terrific job," Bruce said. "I'm sad to see another manager go. It is really disappointing, and it's happening too often now.
"I never thought I'd see the day but it's now becoming like it is in Europe and South America.
"In fact, we're probably worse now. The average [managerial] lifespan, as we keep getting told from the LMA [League Managers Association], is 13 months, and now another good young manager has lost his job.
"To be honest, looking from the outside, I don't know how much more he could have done. In terms of results, he's been terrific."