Spurs host United and the former United skipper believes the Red Devils will score at least one goal at White Hart Lane.
"If Tottenham are going to win today then they better have a couple of goals in them because Manchester United will definitely score," Keane wrote in his column for the Sun.
"Nobody doubts Spurs are a good side but history will show you that they don't get enough results against the big teams - and I can't see that changing this afternoon.
"Their mindset is to attack and that's fine against most teams but you can be asking for trouble if you leave yourself open against the likes of United.
"And it's only a week since Spurs conceded five against Arsenal.
"While they were being torn apart by their rivals, United were grabbing one of their trademark late victories at Norwich City."
United kept their title defence on track with a last gasp 2-1 win over Norwich last weekend in a match which saw veterans Paul Scholes and Ryan Giggs get the goals for Sir Alex Ferguson's team.
Some observers have pointed out that United should perhaps be concerned that United are continuing to rely on Scholes and Giggs - who have a combine age of 75 years - to lead their title charge, but this opinion is not shared by Keane.
"People are going on about how odd it is for Paul Scholes and Ryan Giggs to be both on the scoresheet given their age but it didn't surprise me," Keane wrote in the Sun.
"But it's probably not a great reflection on the game today that they can still be so influential.
"Plenty of players have kept going into their late 30s but they've not had the impact that pair have.
"The key to their success is hunger. It was the 90th minute at Carrow Road when Giggsy scored.
"I've said before that United know how to win games and that was another example of it. But the celebrations were telling as well. Giggsy was ecstatic and he was mobbed by the other players.
"I couldn't help be struck by the contrast between that and what I saw at Nottingham Forest on the Saturday.
"Forest are a proud club fighting for their lives at the bottom of the Championship. Dexter Blackstock scored to put them 2-1 up away to Birmingham City and some of their players didn't even bother going over to congratulate him.
"I couldn't believe it. I still get angry talking about it now. Do they not care? They looked like they couldn't be bothered running across. It's not as if they were 4-0 down and it was a consolation. It was an important goal.
"Those players haven't won a medal between them and yet Giggsy and Scholesy, who have probably 15-20 each, are getting more excited by winning. Shouldn't it be the other way around?
"That's why they're still going when they are aged 38 and 37.
"Alex Ferguson clearly believes United have a better chance of winning if Giggs and Scholes are in the side and that's why they're likely to start at Spurs.
"It was going to be an open game anyway because of the way the two sides play but, because Scott Parker is suspended, it should be even more so.
"I'd be surprised if there weren't at least two or three goals and I'd be surprised if United don't win."
The last time Tottenham beat United was in 2001 when a brace from Willem Korsten and strike from Les Ferdinand gave the Londoners a 3-1 win.
United will also have plenty of motivation for Sunday's clash as only a win will allow them to keep pace with Barclays Premier League leaders Manchester City, who beat Bolton 2-0 on Saturday.
Team News Tottenham v Man Utd
Tottenham manager Harry Redknapp is confident Gareth Bale will be fit despite missing the Gary Speed memorial match between Wales and Costa Rica. Kyle Walker is fit despite suffering an ankle injury against Arsenal last week and Redknapp is also confident that Rafael van der Vaart (calf) and Ledley King (knee) will feature. Scott Parker is suspended following his sending off at the Emirates Stadium last weekend.
Chris Smalling is Manchester United's only doubt after he required stitches in a head wound sustained playing for England. Wayne Rooney has recovered from a throat infection but Antonio Valencia (hamstring), Tom Cleverley (ankle) and Michael Owen (thigh) are all out.
Last season: Tottenham 0-0 Man United, Man Utd 2-0 Tottenham
Last five league matches: Tottenham L W D W L; Man United W W D W W
Top scorers (all competitions): Jermain Defoe (Tottenham) 12; Wayne Rooney (Man Utd) 22
Referee: Martin Atkinson.