While Bayern have gone from strength to strength under new coach Pep Guardiola, successfully defending their Bundesliga title in record time, United have endured a torrid season under their new manager, David Moyes.
United are currently 17 points off the pace in the Premier League and probably need to win the Champions League to qualify for next season's competition, but Giggs says that they are undaunted by the prospect of facing Bayern in Tuesday's first leg at Old Trafford.
"Bayern are a fantastic team," said the midfielder at Monday's pre-game press conference.
"They are the holders and Pep Guardiola has taken over and added a few new players, and they are a very strong team.
"They're the favourites in most people's eyes
But we are Manchester United and at Old Trafford we have had so many great nights.
"We don't see ourselves as underdogs; we see ourselves as Manchester United playing at home
It is going to be tough, but it is always is in the quarter-finals of the Champions League
We are looking forward to it."
Giggs, 40, is the only surviving member of the United team that famously stunned Bayern with two injury-time goals in the final of the 1999 tournament in Barcelona.
He has now taken up a player-coach role, but when he was asked by a journalist if he could ever see himself succeeding Moyes, he was prevented from answering by the United press officer.
United's struggles have seen Moyes's position come under scrutiny in recent weeks, particularly in the light of 3-0 losses at home to both Liverpool and Manchester City.
However, the Scot was bullish when asked about the prospect of taking on Guardiola, who led former club Barcelona to victory over United in the final in both 2009 and 2011.
"I am really looking forward to coming up against him," Moyes said.
"It is the first time I have done, but I have no doubt I will be doing it many times in the future."
- Giggs 'not sulking' -
Giggs, seated beside Moyes in a suite at Old Trafford, also sought to play down media speculation that he had fallen out with the former Everton manager.
The Welshman's appearance in the 3-0 win over Olympiakos in the last 16 was his first start in seven weeks, but he said that he was happy to be used sparingly.
Asked about his relationship with Moyes, he said: "The relationship is good
Of course, as a player you want to play all the time.
"I normally play every two or three weeks to get the best out of me
The last game was probably my first for seven weeks, but you are not sulking
You just have to be ready to play your best for the team.
"There is no problem with the manager
I don't know where that came from."
Giggs is the oldest player to have scored in the post-1992 incarnation of the Champions League, having found the net against Benfica in September 2011, and he said that he had not decided whether this will be his last season in the competition.
"I don't know
I'll tell you after tomorrow (Tuesday)!" he joked.
"I am just trying to enjoy this season and then at the end I will take stock and see what I want to do."
Moyes, meanwhile, gave short shrift to a question about Bayern midfielder Toni Kroos, with whom United have been linked in the British media.
"I don't know where you have your information from, but I think Bayern Munich have a lot of good players; not just Toni Kroos," he said.
United have injury doubts over Rafael and Tom Cleverley, both of whom missed Monday's pre-match training session, while Juan Mata is cup-tied and Robin van Persie has been sidelined by a knee injury.
Source : AFP
Source: AFP