Alaba has announced he will leave Bayern at the end of the season when his contract expires and has been strongly tipped with a move to Madrid.
Kimmich has endorsed the proposed transfer, saying Alaba has earned the right to move to the Spanish giants.
What was said?
"He has won everything here multiple times," Kimmich told Sky Germany. "Twice the triple, once even six titles in one year. Real is in any case a worthy club.
"There aren't many steps you can take after playing for Bayern but Real Madrid isn't that bad as the next step."
Alaba's trophy-filled Bayern career
The 28-year-old has won everything possible at Bayern since moving as a youth player from Austria Vienna.
Alaba has won a grand total of 26 trophies during his time at Allianz Arena, including nine Bundesliga titles and two Champions League crowns.
Kimmich's own future in doubt
On Saturday, Goal and Spox reported that Kimmich has split with his agent and will now represent himself in future contract negotiations. The move increased speculation around the 26-year-old's future, as he could seek improved terms on a contract that runs out in 2023.