Bild was the first to report about Boateng's rejection of United on Tuesday.
Paris Saint-Germain is linked with the 2010 World Cup victor.
With Bayern 4-0 up thanks to a Robert Lewandowski hat trick and a goal from Kingsley Coman, Alaba tangled with Eintracht's Danny da Costa and had to leave the pitch after prolonged treatment.
The Red Devils are widely reported to be looking at a possible defensive signing before the close of the summer transfer window in the Premier League.
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Pundits say Boateng is very interested in joining PSG and has rejected an offer made by Manchester United.
Bayern recently sold Arturo Vidal to Barcelona and chairman Karl-Heinz Rummenigge appeared open to further departures - a mistake, according to Robben. 22-year-old Benjamin Pavard is rumored to have already signed an agreement with the Munich outfit during this summer's World Cup in Russian Federation.
"The manager is obviously not happy about the signings he hasn't been able to make and not having certain players available on their pre-season tour, which isn't nice to hear if you are a young kid trying to make your mark on the fringes of the squad". The French defender is said to have taken advantage of a 2019 exit clause at his current club VfB Stuttgart.
The 29-year-old has been touted as a potential candidate to improve Jose Mourinho's defence ahead of the new Premier League campaign.
Robben is concerned about the team's success and said, "We must avoid being our own enemy", before adding that Boateng is one of the world's best defenders, "and we need his quality". Since 2016, Boateng has been sidelined with muscle injuries on several occasions. The player said the accusations were a great disappointment but he admitted to intensifying his rehabilitation. Some reports suggested he and other players had become complacent, and that a new impulse was needed.