The two Manchester clubs sit at the summit of the Premier League table with just goal difference separating them, but the midfielder insists the main challenge comes from London
United’s neighbours Manchester City have made an impressive start to their campaign, and with the financial backing of billionaire Sheikh Mansour, Roberto Mancini's side have been propelled into the title race.
While United are only above their local rivals at the top of the Premier League after seven games on goal difference, the 37-year-old is adamant that Chelsea will be their most dangerous challenge as a team.
"It is strange to see Manchester City, especially if you think about the last 20 years where Manchester United have won numerous trophies," the United veteran told reporters.
"But the situation has changed. They have plenty of money so they have some outstanding players.
“But I think Chelsea are more dangerous as a team."
The Welshman also insisted that his side are capable of beating Barcelona in the Champions League, following two defeats in three years to the Spanish club at the final stage.
"I don't think Barcelona are unbeatable," he added.
"They have a really strong team but it's not impossible to beat them. But I don't argue that Barcelona are the best team in the world at the moment. It is a challenge for us to reach their level.
When questioned on his future, Giggs simply added: "My next aim? To win the next game and then the following one. That's all. I don't like too far targets.
"I'm sure I'll stay in football after retiring because this has been my world since I was 15 years old. I enjoy football as much as I enjoyed it 15 or 20 years ago."