Rafinha joined Bayern from Genoa in 2011, but he struggled for regular football last season and there had been reports he could be on his way out in the summer.
However, he has impressed under Pep Guardiola at right-back this term following Philipp Lahm's move to a central midfield role.
The 28-year-old's present deal expires at the end of the campaign and the Brazilian is hoping he will be kept on by the European champions.
"Of course, I am delighted to be a Bayern Munich player," Rafinha told kicker-Sportmagazin.
"Bayern Munich is the best club in the world, playing for this club is truly a dream come true.
"I would be very happy to be able to stay on at the club beyond the end of the season."