David Moyes’ side currently sits sixth after an indifferent start to the season, seven points behind the table-topping Gunners.
But Giggs believes that despite United's 2-2 draw with Cardiff on Sunday, it retains a good chance of retaining its league title.
"It has been a disappointing start,” the Welshman told Talksport. “The last 10 games have not been too bad – I think we were unbeaten in eight or nine games – but [Sunday] was a game we should be winning.
“Only Arsenal – who are up there and deserve to be up there - have shown consistent form. It’s been a crazy season, we need to hang in there when we’re not playing at our brilliant best and get a run together. The team that does that will have a great chance of winning league.”
Giggs has made 951 appearances for the Red Devils since exploding into the first team as a fearless, fleet-footed winger in 1991.
The veteran says he sees something of himself in Adnan Januzaj, the latest wonderkid to grace Old Trafford.
“He takes the ball and has good balance and is exciting - like when I first got in the team. He’s an exciting player for the fans and for the other [first-team] players and academy players,” Giggs added. "They can look up and see it’s possible to make it in the first team if you work hard and in the right way.
“I think he’s got about seven or eight countries that he can choose from. I tried to nick him for Wales but he’s not interested!”