Louis van Gaal could lose his job if the German side are knocked out of the Champions League on Wednesday night.
Bayern are third in Group A with just four points from four games as they prepare to face Israeli side Maccabi Haifa. Things are not much better in the German league, in which Van Gaal's seventh-placed side have won just five of 13 matches.
Job offers: Guus Hiddink could leave Russia
The poor performance has led to criticism of former Barcelona boss Van Gaal from directors and senior players such as Philipp Lahm.
Bayern accept that star player Franck Ribery and others may leave if they cannot compete with Europe's finest and former Chelsea boss Hiddink has been identified as the man to turn around their fortunes.
The club's director of sport ChristianNerlinger has increased the pressure even further by insisting Bayern must win theremaining four Bundesliga fixtures before Christmas.
Nerlinger will assume even more power at the club when generalmanager Uli Hoeness steps up to become club president this Friday, and one of his duties will be the hiring and firing of coaches
'You have simply got to win the four remaining games before the winter break,' said Nerlinger. 'The curve has now got to turn sharply upwards.
Struggle: Anatoliy Tymoshchuk (left) has struggled in a new position at Bayern Munich
'Teams like Mainz cannot be allowed to remain above Bayern in thelong term. Van Gaal knows the job, but he now needs to get thingsright.'
Heading for the exit: Luca Toni is not happy at Bayern Munich
Van Gaal's struggle to stamp his authority in Bavaria has seen himsuspend Italy striker Luca Toni, according to reports in Germany.
Tonihas criticised the boss after falling behind Mario Gomez, MiroslavKlose and Thomas Mueller in the pecking order and Van Gaal has hadenough.
In his latest outburst, Toni said: 'For four months, I have had a problem with Van Gaal. Everything has borders and our relationship is nearly at the end.
'I would like to return to Italy so I can start scoring goals again and get back into the national team.'
Hiddink, 63, is mulling over whether to accept a two-year contract extension with Russia following their failure to qualify for next summer's World Cup finals.
He has also been linked with a return to Stamford Bridge as technical director while PSV Eindhoven are believed to have offered him a boardroom role.
They are not the only suitors, but the Dutchman has ruled outlinking up with Nigeria or stepping in to help Diego Maradona andArgentina for South Africa 2010.
Under pressure: Louis van Gaal has seen his Bayern side underperform
'I'm not going to the World Cupin South Africa as a coach,' said Hiddink. 'I couldn't get there withthe Russia team and it would be unfair to Russia's players for me go tothe tournament with another team.'
The decision on his future could come down to who is voted in as the next head of the Russian FA in February, but outgoing FA chief Vitaly Mutko wants a decision in weeks rather than months.
'We agreed with Guus that he would decide as soon as possible,' said Mutko. 'We agreed to meet again before the end of the year and come to a decision.'
Chelsea poised to welcome back Guus Hiddink as Russia coach targets roleVilla tells Chelsea, United and Man City he will consider £35m Valencia exit'Chelsea feel invincible' - John Terry believes Blues can win it all this seasonChelsea's starlet Gael Kakuta is ready storm Porto's 'Dragon's Den'CHELSEA FC