Eriksson was the referee who earned the wrath of Manchester City manager Manuel Pellegrini for his decision-making in City's 2-0 loss to Barcelona in the last-16 first leg in February.
Pellegrini was particularly unhappy that Eriksson awarded a penalty to Barcelona for a foul by Martin Demichelis on Lionel Messi that was shown to be outside the box, while he felt there was a foul on Jesus Navas in the build-up.
Pellegrini said: "From the beginning I felt the referee was not impartial to both teams so he decided the game with a foul that he didn't whistle against and a penalty with Demichelis that was not a penalty - it was outside the box.
"He did not have any control of the game. He was on the side of Barcelona from the beginning until the end.
"I think it was not a good idea to put a referee from Sweden in charge of such an important match, especially a referee who has made an important mistake against Barcelona in a previous match."
Pellegrini appeared to be referring to the 2012 Champions League quarter-final when Eriksson was criticised by then-Barcelona coach Pep Guardiola for failing to award his side two penalties against AC Milan in the goalless first leg at the San Siro.
Pellegrini apologised for his comments later the same week, claiming he did not intend to accuse the referee of bias or disparage Sweden.
His apology was not enough to save Pellegrini from a UEFA sanction, with the governing body handing him a three-match touchline ban, one of which was suspended.
Eriksson, 40, has been a professional referee for 20 years and has been selected for this summer's World Cup finals in Brazil.
United and Bayern drew 1-1 in the first leg at Old Trafford last week, with Nemanja Vidic and Bastian Schweinsteiger, who was later sent off, scoring the goals.