"Alex has done a fantastic job there, hasn't he? I was at Bournemouth when I first met him 20-odd years ago and the team he's put together now could be one of his best," said the Pompey boss.
"He's up there with all the great managers; Cloughie, Shankly, Busby - all the greats.
Redknapp is expecting Portsmouth's latest trip to Old Trafford to be a difficult one.
"We will go up there and try to give them a right go. These games against the top four are bonus games for us now," he added.
"If you are near the bottom of the league the prospect of going up to United can be frightening but we are in no danger of relegation now, we're playing well away from home and it is something to look forward to.
"Ronaldo's fantastic, Rooney, too, and Carlos Tevez. They can rip you to pieces if you are not careful.
"But we've got a good squad now even without the four lads (Papa Bouba Diop, Kanu, John Utaka and Sulley Muntari) away in the African Nations Cup. We'll be very strong when they come back.
"Lassana Diarra has come here from Arsenal and shown already that he's world class. We already have an outstanding goalkeeper in David James and a top full-back in Glen Johnson - who I think should both play for England.
"We've also got a terrific loan signing in Milan Baros, who has every chance of making his debut, and Sol Campbell should be fit to come back into defence, so we're not lacking quality."