The midfielder made his debut for the Bavarians in 2002 and has not ruled out the possibility of remaining at the Allianz Arena until the end of his career.
At 29, Schweinsteiger, who has won six Bundesliga titles with the club, 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 but the Germany international feels that he is of similar stock.
"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 my 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 title, while they are also hoping to become the first club to secure back-to-back Champions League crowns.