Bayern Munich coach Vincent Kompany has been discharged from hospital five days after collapsing during a training session, but there is no timetable for his return as he continues to recover from a medical condition affecting the membranes around his brain and spinal cord.

Bayern sporting director Max Eberl confirmed Wednesday that the 40-year-old Belgian had been diagnosed with meningeal irritation, which can develop into meningitis if left untreated.

Kompany had been feeling unwell for several days before collapsing while observing a training session involving the club's reserve team last Friday. An emergency doctor was called to the scene.

"He is doing as well as can be expected," Eberl told German broadcaster ARD. "He has been discharged from hospital today, which is the biggest and best news for all of us."

Kompany will continue his recovery at home, where he is expected to get the rest he needs before returning to work. Eberl said the condition was an illness rather than a consequence of the pressures associated with managing one of Germany's leading clubs.

"It is an illness. Anyone of us can get it. It has nothing to do with the pressure we face in the Bundesliga," Eberl said.

Assistant coach Aaron Danks has taken charge of Bayern's first team in Kompany's absence and said there was no indication of when his manager might return.

Speaking after Bayern's 6-1 victory over second-division Magdeburg in the German Cup's second round on Wednesday, Danks described Kompany's discharge as an encouraging step but stressed that his health remained the priority.

"It's obviously a really positive step in his road to recovery," Danks said. "He gets to settle back at home now, be closer to his family, be closer to his home comforts, but it's still really important that he takes his rest and he recovers."

Danks said he had not spoken to Kompany for a couple of days, adding that the club's medical team would continue to monitor his progress.

"So there's no timescale on it, nothing that I've been told," Danks said. "Our doctors will continue to work closely with Vince and, at the right moment, he will be back with us once he is fit and healthy to do that. And we look forward to that day."

Kompany has now missed two consecutive matches, including Sunday's 3-1 Bundesliga victory over Freiburg, which Danks also oversaw. Bayern will continue under the assistant's leadership until further notice, potentially including Saturday's high-profile home clash against Borussia Dortmund.

The meeting, known as Der Klassiker, is one of the Bundesliga's biggest fixtures, with both clubs competing near the top of the standings.

Eberl described the situation as a difficult period for Bayern, which is also dealing with the absence of influential midfielder Joshua Kimmich following the death of his father.

"You notice how the club is coming together," Eberl said, highlighting the solidarity within the squad and staff as they support Kompany through his recovery.