Jerome Boateng's role in Bayern Munich's American tour ended early at the weekend. Photo: Michael Dalder/Reuters

HOUSTON  Defender Jerome Boateng's role in Bayern Munich's American tour ended early at the weekend after the Bundesliga champions gave him permission to return to Germany "for private reasons."

The 30-year-old former Germany international was considered a transfer candidate but has impressed during close season so far. He returned home late after Saturday's 3-1 win over Real Madrid in Houston.

"From a sporting view I am very happy with him, not only with the performance he delivered today," said Bayern coach Niko Kovac. "That was like as I know him, as we all know him. A big compliment. He had already shown that in training."

Bayern chairman Karl-Heinz Rummnigge also commented positively on the world champion from 2014. President Uli Hoeness had previously suggested a transfer towards the end of last season.

"He has done well, he has prepared perfectly for this trip," said Rummenigge. "He came with ideal weight and a certain fitness already."

Boateng's future remains uncertain despite his contract having two years to run in Munich.

"The last word definitely hasn't been said," said Rummenigge.

But Bayern are well stocked in Boateng's position with club record signing Lucas Hernandez, Niklas Suele, Benjamin Pavard and even midfielder Javi Martinez capable of playing there.

"We will see what happens in the transfer market," said Rummenigge. "Then we will finally speak with him about how we go on."

Bayern lost the first game of their tour to Arsenal but goals from Corentin Tolisso (15th minute), Robert Lewandowski (67) and Serge Gnabry (69) earned victory over Real in front of 60,413 fans.

Sven Ulreich was sent off for a late foul on Vinicius and Rodrygo grabbed a consolation for Zinedine Zidane's side from the resulting free kick.

"I think that Bayern even now have a top first eleven already," said Real's former Munich midfielder Toni Kroos. "I always see Bayern right up there."

Bayern conclude their pre-season tour against AC Milan in Kansas on Tuesday. They open the new Bundesliga campaign at home to Hertha Berlin on August 16.