The Germany midfielder made his Bayern debut in 2002 and has not ruled out the possibility of remaining at the Allianz Arena until the end of his career.
At 29, Schweinsteiger still has a long way to go until he can match the longevity demonstrated by Manchester United's Giggs, 40, and Roma's 37-year-old maestro Totti.
Nonetheless, they are comparisons that he is comfortable in making.
"Can I be compared to Francesco Totti or Ryan Giggs? Yes, absolutely," Schweinsteiger 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.
"Will I terminate my career at Bayern? It is impossible to reply.
"Here I am more than happy, but there could be surprises in the future. Moreover, I still have a few years to go on playing."
Bayern are closing in on a 23rd Bundesliga crown and retain hope of becoming the first club to secure back-to-back UEFA Champions League crowns.
Schweinsteiger has won six league titles with the club.
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