Karl-Heinz Rummenigge warned Leroy Sane must show more desire and says Bayern Munich will be prepared to "kick his butt" if needed to get the best out of their big-money signing.

Sane has endured a difficult start to his time at Bayern and hit a new low when he was hauled off after being introduced as a substitute to replace the injured Kingsley Coman in the first half of a dramatic 2-1 win at Bayer Leverkusen on Saturday.

The winger, signed on a five-year deal for an initial fee of €49million (£44.5m) - rising to €60m (£54.5m) - from Manchester City in July, spent just 36 minutes on the field at BayArena.

Sane had been criticised by the great Lothar Matthaus ahead of the game and Bayern coach Hansi Flick also said the 24-year-old must offer more in order to force his way into the team.

The Bundesliga champions' chief executive Rummenigge says Sane has to raise his game and work harder to be a success at the club, who on Sunday revealed Coman's hamstring injury is not serious.

He told SPORT1: "Leroy was not happy [to be taken off], that's clear and understandable. God gave him incredible talents. I only believe one thing: he has not yet reached this FC Bayern gene.

"Like Thomas Muller, he was my hero yesterday. He has marched up and down, but not as protected by talent as Leroy. He has to work on that, that is his job.

"We have done everything we can to ensure that he comes to Bayern. We encourage every player, but we also challenge. He has to internalise that and the team supports him.

"He has to take the next step, Leroy has to adapt his character to FC Bayern. This character is: you forgive everything, but you have to give the impression that you are throwing everything into the balance in order to leave the field as the winner. He will have to learn that."

Rummenigge added: "I believe that he can have a big future at FC Bayern. We are ready to help him, to encourage him, but he also has to challenge himself in order to get to where he can be. We will, if necessary, kick his butt to get him there."

Sane lost possession nine times in his short time on the field, completed 15 of his 19 passes (78.9 per cent) and conceded two fouls, more than any other Bayern player.

Robert Lewandowski's last-gasp goal, his second of the game, consigned Leverkusen to a first defeat of the season to ensure Bayern will end 2020 two points clear at the top of the table.