Midfielder Giggs made his senior United debut back in 1991 and has gone on to win a host of medals with the English club, including 13 Premier League titles and two Champions Leagues.
When asked whether he would like to achieve similar longevity at Bayern Munich, 29-year-old Schweinsteiger admitted that both Giggs and Roma's veteran attacker Francesco Totti act as an inspiration to him.
"Can I be compared to Francesco Totti or Ryan Giggs? Yes, absolutely," he told France Football. "They are two amazing players. At 40 years of age, Giggs is still going on playing at highest level. He is remarkable.
"I am proud to have been at just one club. Were there any moments I was close to leaving? Yes, several times. But in the end the heart made the decision."
Schweinsteiger has made 461 appearances for Bayern.