Suárez signed a new long-term contract at the Reds in the summer after completing a £22.75m switch to the Merseyside outfit from Ajax in January 2011.
Pep Guardiola is set to take charge of Bayern in the summer, and the former Barcelona boss has been linked with a big-money swoop for the Reds striker.
“I hope [to be at Liverpool] for a very long time because it’s a massive club that kids dream about playing for,” Suárez told Liverpool’s website.
“I’ve been very proud to be at a club like Liverpool and to have made the decision to come here. In two years I’ve lived through some spectacular and very special moments that I will never, ever forget.
“There have been a few difficult times as well, but with the support of my family, the club and the fans, things have gone well for me.
“I do feel at home here. When I’m out and about, all I get is support and encouragement from the local people and that’s very important, and when I come here to the club I feel like people have known me all my life. That also helps a great deal to making me feel so at home.
“I hope to be able to help out the team for as long as I possibly can while trying do something to make the club and the fans very happy.”