Sir Bobby told the Guardian: "I would not sign Jonathan Woodgate if I thought he was a racist.
"I'd rather not have the controversy, but we can't avoid it. We are getting some pretty nasty stuff at the moment, but Newcastle are black and white in every sense. We've got a multinational squad, we work with Kick Racism Out of Football.
"Jonathan is a close friend of Kieron Dyer, Jermaine Jenas and Rio Ferdinand, and that speaks for itself. If we had any inkling that he harboured racist thoughts, we wouldn't have him at this club.
"At the time [of the Hull court case] he looked gaunt, he was off his food and his fitness went down because of it. Perhaps he needs a way out of it, a fresh start, a fresh outlook, a fresh situation around him.
"Moving away from Leeds will be a good thing for him and comes at a good time, too. He's served his sentence and paid his dues in that area. I think he has to be given another chance.
"I've got a clause in my contract saying that I should live within 20 miles of the club and I think players should do the same. We might have to move him, say 'Come to Newcastle. You're paid by Newcastle, you play for Newcastle, come and live in Newcastle'."