Karl-Heinz Rummenigge has said Bayern Munich are not interested in selling Thomas Muller, amid speculation that a trio of Premier League clubs want to sign the Germany international.
According to Sport Bild, Serie A champions Juventus as well as Chelsea, Arsenal and Liverpool all want to purchase Muller, who has slipped down the pecking order at Bayern.
The 27-year-old only managed five Bundesliga goals last term and endured a 999-minute Bundesliga goal drought -- in contrast to his most prolific season ever of 2015-16 when he notched 32 goals in all competitions and was reportedly the subject of a €100 million bid from Manchester United.
"Both the club and Thomas agree on the assessment of last season -- it wasn't a good one," Bayern CEO Rummenigge told Sport Bild. "[But] Thomas is still not for sale because he's a perfect fit for Bayern. This is not a matter of discussion."
Muller played 800 minutes less under Bayern boss Carlo Ancelotti last term than during Pep Guardiola's final season in charge.
However, Rummenigge backed the club's sole remaining Bavarian first-team player to come through his barren spell.
"Thomas knows that he has to deliver a bit more, but this isn't a problem," he said.
Bayern face Arsenal in Shanghai on Wednesday as part of their summer tour of China and Singapore. Both Muller and new signing James Rodriguez are expected to feature for the Bundesliga champions against Arsene Wenger's side.
Speaking at a news conference ahead of the game, Ancelotti said James' versatility means he can provide competition for a number of Bayern's attackers, not just Muller.
"Of course we didn't buy James to replace Thomas Muller. This is clear," Ancelotti said. "Because if you think that you can also think James can replace Thiago [Alcantara], because he has played a lot of times as an offensive midfielder. And since he can also play on the right, you can think we bought James to replace [Arjen] Robben, or to replace [Franck] Ribery because he can play also on the left.
"We didn't buy James to replace anyone; we bought him to have a better team. And also, James knows that if he doesn't deserve to play he doesn't play, he goes on the bench -- as a lot of players go, because we have a lot of competition in the team. He has no place guaranteed from me. If he deserves to play, he will play."
Seated next to Ancelotti at the news conference, Muller echoed his coach's sentiment about James bolstering the all-round quality of Bayern's squad.
"Personally I think James is a very good player who will improve our team quality and help us reach more goals," Muller said. "With James joining the team we have more options to choose from. He's an excellent midfielder and he will bring supplementary support to the team.
"The coach is lucky to have so many players available in attack. But it's up to the coach to decide who plays in March, April or May and he's sitting here."
Meanwhile, former Bayern sporting director Matthias Sammer has told Eurosport that Muller is an essential part of the club's future but he needs patience in order to succeed.
"Thomas Muller, along with one or two others, for me, is the soul and the future of FC Bayern. And the club needs to understand that too. A player of his type is unique in the world," he said.
"However, in the present time, he needs to feel that Bayern have faith in him too in order to shape a stable future. That is an important task for the leading figures at the club.
Sammer, who worked with Muller between 2012 and 2016, added that Muller is "an irrational player who at times drove Pep [Guardiola] to distraction. He can suddenly disappear from a game, that's the way he plays.
"Thomas is a free spirit and has to feel this freedom.
"He is so important. He is an idol, an extremely vital integration figure for the future of the club."
However, Sammer is not as enthusiastic about Bayern's new signing James Rodriguez despite his popularity on social media.
"He has a few defects," Sammer said. "He is not the quickest, fundamentally he is not the most athletic player either. He's not the most physically robust of players. Of course, in his position he has a certain limitation too.
"This versatility, which sounds interesting, I don't see it in him because he can't play on the wing as he lacks tempo.
"It's excellent this social media and a lot of fuss. That's all very well but as a sportsman, where we focus on performances, I prefer the value of Thomas Muller."