The Ukrainian, who has been at the club for three years since arriving from Zenit St Petersburg in 2009, only has one year left on his current deal at the Allianz Arena.
Tymoschuk told Kicker magazine that a return to Russia could be on the cards, though he did not rule out staying at Bayern altogether.
"Maybe I'll stay in Munich, I do not know yet," said Tymoschuk. "[I have] a few options in Russia and contact with several clubs."
Last season's Champions League finalists Bayern are reportedly trying to sign Spain and Athletic Bilbao player Javi Martinez who, like Tymoschuk, can play in both defence and midfield.