The former Red Devils striker is one of three options for the German side
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Ole Gunnar Solskjaer is reportedly one of the managers Bayern Munich would consider appointing if they sacked Thomas Tuchel.
The Norwegian is one of three candidates being discussed internally having been out of work since leaving Manchester United in November 2021.
Tuchel is under increasing pressure at Bayern following Sunday's shock Bundesliga loss away to VfL Bochum.
The German side have now tasted defeat in their last three matches in all competitions and are eight points behind league leaders Bayer Leverkusen.
Ole Gunnar Solskjaer is being considered by Bayern Munich as an interim boss
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Bayern lost 3-0 to Leverkusen nine days ago before going down 1-0 in the first leg of their Champions League last-16 tie against Lazio.
But the defeat at Bochum is a new low for Tuchel and he could be fighting for his future at the Allianz Arena.
Bayern CEO Jan-Christian Dreesen confirmed on Sunday that Tuchel will still be in place for Saturday's match against RB Leipzig.
Dreesen admitted: "I feel rubbish. I don’t believe in big statements about the coach. This issue isn’t on our mind at the moment."
Bayern have won the Bundesliga 11 seasons in a row but could now see out an entire campaign without silverware.
Sky Sports in Germany claims that club chiefs are already considering their options if they were to sack Tuchel.
Solskjaer is being considered as a potential interim boss if they feel they should fire Tuchel before the end of the season.
The 50-year-old spent almost three years at United, winning 91 of his 168 matches in charge with a win percentage of 54.17.
He was unable to win any trophies during his time with the Red Devils, losing in the 2021 Europa League final.
Bayern sporting director Christoph Freund knows Solskjaer well but there is yet to be any concrete contact.
The No 1 target for Bayern if Tuchel was to leave is Leverkusen's Xabi Alonso.
The Spaniard, widely tipped to be Liverpool's preferred candidate to replace Jurgen Klopp, spent the last three years of his playing career at Bayern.
Alonso has built a reputation as one of the brightest up-and-coming coaches in Europe.
Bayern are also interested in former Real Madrid manager Zinedine Zidane.
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Xabi Alonso is the No 1 target for Bayern Munich
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Zidane has only managed Real, with his second spell at the Bernabeu ending in 2021.
The Frenchman won two La Liga titles and three Champions Leagues during his time with Los Blancos.
Meanwhile, Tuchel claimed Sunday's 3-2 loss at Bochum was not a fair result on his team.
He said: "I don’t think today’s defeat was fair, I think a lot went against us today.
Thomas Tuchel's job at Bayern Munich is safe for the time being
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"I think we had an expected goals (xG) value of 3.4 and we had four, five, six top chances.
"We completely dominated the game and actually went behind out of nowhere.
"We never stopped putting in the effort until the end and then played with a man down for a long time.
"A lot went against us today. I feel today’s defeat is different to the last two."