United are unbeaten in the league this season but have drawn more games than they have won.
They have also been at the centre of one of the most extraordinary footballing sagas of recent years, which ended when Wayne Rooney finally signed a new five-year contract last week.
Rooney looked set to leave Old Trafford after publicly questioning the club's ambition, amid concerns they had been in decline since the departures of Cristiano Ronaldo and Carlos Tevez.
But Spurs boss Redknapp believes once Rooney recovers from an ankle injury and rediscovers his form, Sir Alex Ferguson's men will be back on track.
"They've had a few problems, haven't they, obviously losing Rooney with his injury and then another few problems they've had with Rooney," Redknapp said.
"When he comes back firing on all cylinders, they'll always be there.
"They've got a fantastic manager; he gets the best out of them every year; they produce great teams and I wouldn't write them off.
"They'll be right again there pushing all the way for the championship.
"Chelsea are obviously favourites at the moment but I don't think Man United will be too far away again come the end of the season."
Tottenham will face a Rooney-less United on Saturday, and Redknapp admitted that was a prospect he would relish.
"I'd be a liar if I said otherwise," he said.
"I'd rather see Rooney's name not on the team-sheet any day of the week."
Spurs appear to need all the help they can get winning at Old Trafford if their recent record there is anything to go by.
It is almost 21 years since they last tasted victory there in any competition.
Redknapp joked: "I wouldn't take the blame for what happened in '89 or '90, or '91, '92, '93, or all those other years.
"It's a hard place for anyone. How many teams have been there and won?
"They lose one or two home games a season at the most.
"And it's different players here now.
"They wouldn't know about that record or anything else.
"It's a new experience for some of them."
Spurs have made great strides during Redknapp's two years in charge but he has yet to halt their 17-year winless run at the grounds of the so-called 'big four'.
"We need to go away from home and play at Chelsea, Arsenal, Liverpool, Man United and pick up a win," he said.
"We did it at Man City last year, obviously, and I think they'll probably be a top-four team this year.
"But we need to go away from home in one or two of those games and pick up better results this year than we have in the past.
"A lot of it is belief, believing that you can go there and get a result. If you go there and you're negative about it, you won't.
"We'll go there tomorrow with a team looking to take the game, if we can, to Man United.
"We're not going to go there and shut up shop completely.
"We've got talent and we'll look to go there and do our best to attack them at every opportunity that we get."
Redknapp is pondering resting Gareth Bale ahead of Tuesday's Champions League clash with Inter Milan.
"We've got two big games and I'll look at it," Redknapp said.
"He's had a really hard spell of playing game after game."
Redknapp, who gave Bale as few days off this week, joked: "He went abroad - he went to Cardiff!
"He could have gone away, a few days abroad or something, but he just wanted to spend a bit of time with his family."