The Red Devils have been in good form so far this season but suffered their first loss of the campaign last weekend when they were beaten 2-1 by newly-promoted Huddersfield on Saturday.
Manchester City, meanwhile, have been in superb form this season and are currently five points clear at the top of the Premier League table after their strong start.
The two Manchester club look as though they will be serious contenders for the title this season in what looks set to be a thrilling race.
And former Manchester United star Giggs believes that it’s crucial that the Red Devils do enough to keep themselves in the mix for the title as the season continues.
Speaking to Sky Sports, Giggs said: “Manchester City are obviously still flying with their results and performances but I think they’ll have their problems.
“They’ll have their sticky patches and United just need to be hanging onto their coat tails and ready to pounce.
“The fear is that United are not in the place to pounce when Manchester City slip up.
“They have tough games coming up, with Tottenham, Chelsea and Arsenal before the Manchester derby in December.”
Manchester United will look to get back to winning ways in the Premier League when they take on Tottenham at Old Trafford this weekend.
Spurs head into that game fresh from their impressive 4-1 victory over Liverpool at Anfield on Sunday, a result which left them level on points with Manchester United in the table.
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