The clash of two of Europe's biggest clubs will forever revive memories of their epic 1999 Champions League final in Barcelona when United scored twice in stoppage time to beat the German side 2-1.
FC Bayern Munich won on their last trip to Manchester United F.C. when they beat City 3-1 in a group match in October and a repeat of that scoreline would almost certainly set up Pep Guardiola's team to reach the last four.
But Giggs, who played in the final 15 years ago, remains confident of a Manchester United F.C. success against opponents who wrapped up the Bundesliga title last week.
"Obviously FC Bayern Munich are a fantastic team," said Giggs, who will move to within one of Raul's record total of 142 Champions League appearance if he plays on Tuesday.
Now player-coach at Old Trafford, the 40-year-old Welshman told reporters: "They're the holders and Pep Guardiola's taken over and added a few new players and they're a very strong team.
"They're obviously favourites in most people's eyes but we're Manchester United at Old Trafford and we've seen so many good nights there, in Europe especially.
"So as players we don't see ourselves as underdogs, we see ourselves as Manchester United F.C. playing at home in the Champions League.
"We can't wait. These are the games that you want to be involved in as a player. We'll go out there and, yes it's going to be tough, but we're confident."
Although they have endured a difficult first season under David Moyes and are seventh in the Premier League, Manchester United F.C. have won all four home matches in the Champions League.
Guardiola, however, steered Barcelona to two Champions League final victories over United in 2009 and 2011 and while he has vast experience of this competition, Moyes is taking charge of a team at the quarter-final stage for the first time.
Moyes echoed Giggs's optimism, although experienced left back Patrice Evra is suspended and will miss the chance to renew his rivalry with Bayern's Arjen Robben.
"We know that on our day we're as good a side as any but we have to show it more often," Moyes said.
"I've got great belief in the players and I've said that from day one - that hasn't changed.
"I get the feeling the players all want to play, I can tell that from their attitude in training. They all want to play in the big games, that's what the players here have wanted to do over the years."
Moyes will also be without the injured Robin van Persie while full backs Rafael and Alex Buttner are struggling to be fit. Defenders Rio Ferdinand, Chris Smalling and Jonny Evans all trained on Tuesday.
"We have defensive issues, undoubtedly," Moyes added.
"But I won't be giving out my team today, certainly not to Bayern or to you (the media), but we will have to make one or two changes."
Manchester United's form has been erratic recently with 3-0 home defeats by Liverpool F.C. and Manchester City mixed in with three-goal winning margins over West Bromwich Albion and Aston Villa in the league and Olympiakos Piraeus in the Champions League.
Manchester United F.C. had their backs to the wall when they faced Olympiakos in the first knockout round two weeks ago going into the match 2-0 down from the first leg but Van Persie's hat-trick sent them through 3-2 on aggregate.