Campbell is set to be hit with a barrage of vitriol from Spurs supporters when he turns out for Arsenal at White Hart Lane.
The veteran centre-back quit Spurs for the Gunners in 2001 and the Tottenham faithful have never forgiven him.
Redknapp knows he cannot prevent loyal Spurs followers venting their fury towards Campbell, who is in his second spell at Arsenal, but hopes the insults do not go too far.
"I'm sure he will get some grief. It is no good me sitting here and saying that he won't," Redknapp said.
"They (the fans) pay their money and they are going to do what they want to do, aren't they? I just hope they don't do anything silly or shout anything silly.
"Sure, if they want to jeer him or whatever, that is fine. But we saw trouble before at Portsmouth with people making remarks that aren't right. You do not want that."
Spurs fans attacked Arsenal's team bus when Campbell first returned to the Lane in 2001 before subjecting him to homophobic chants when he played for Portsmouth against Tottenham at Fratton Park in 2008.
It will therefore not be the first time he has faced the wrath of his former club's supporters and Redknapp believes Campbell, who played under him at Portsmouth for two years, can cope.
"He is used to it now, I suppose," Redknapp said.
"When he plays, he gets on with it, doesn't he? He will get on with the game. He has been through it all before and he is experienced enough now.
"It has been a long-running saga but they have got the hump with him here and they are not going to forgive him."
Spurs will be without Aaron Lennon, who suffered a setback in training on Monday as he bids to overcome a groin injury that he first sustained in December.
Midfield anchorman Wilson Palacios begins a two-match suspension while Niko Kranjcar could struggle to return again this season after injuring his ankle in Sunday's FA Cup semi-final defeat to Portsmouth.
A win for fifth-placed Spurs will see them narrow the gap to fourth-placed Manchester City to one point with five matches left.