Bayern Munich demonstrated its insatiable desire for silverware on Tuesday by thrashing Olympiakos 4-0 with 10 men to reach the Champions League knockout stages as group winner.

Bayern raced into a 3-0 lead after just 20 minutes at Allianz Arena thanks to goals by Douglas Costa, Robert Lewandowski and Thomas Mueller before defender Holger Badstuber was sent off.

The Germany defender marked his first start in seven months after injury by earning a red card, but Bayern barely broke stride as France winger Kingsley Coman notched its fourth goal.

Bayern is eight points clear at the top of the Bundesliga and looking strong in Europe after clinching top spot in Group F with a game to spare.

The Bavarians have made no secret of their desire to win the treble of Bundesliga, German Cup and Champions League with coach Pep Guardiola in the final year of his current contract.

"We are always hungry, which we saw again tonight," said Bayern's sporting director Matthias Sammer.

Few teams will fancy facing Bayern in the knockout rounds, but captain Philipp Lahm said it was important for his side to ensure it progressed in first place, thereby avoiding a last-16 clash with other group winners - including Barcelona.

"It's always important to finish first," said the ex-Germany skipper. "It brings the advantage in the last 16 that you play the second leg at home. It's a good way to finish."

Sammer said he disagreed with Swedish referee Jonas Eriksson's decision to show Badstuber a straight red for bringing down Nigeria international Brown Ideye, who was through on goal, with 53 minutes gone.

"For me that was no sending off, I wouldn't have blown the whistle," Sammer said.

Badstuber will miss Bayern's final group match away at Dinamo Zagreb in two weeks.

Meanwhile, Olympiakos remains second in the group, and a draw at home to Arsenal on Dec 9 will guarantee that it goes through at the English squad's expense.

Germany defender Jerome Boateng said his side showed it deserves to be top of the group having also routed Dinamo (5-0) and Arsenal (5-1) at Allianz Arena this season.

"That was again another concentrated performance from us," said the centerback.

"Being first in the group is important and was always our goal. We have confirmed today that we deserve to be first."

The 27-year-old World Cup winner, who joined Bayern from Manchester City in 2011, has a contract until 2018 but says he would be happy to extend that deal.

"I can well imagine that happening. I have always said I feel really good at Bayern," he told Sky TV.