Rodriguez left Real Madrid in the summer after falling out of favour with Zinedine Zidane and he reunited with Carlo Ancelotti, who originally brought him to the Santiago Bernabeu from Monaco in 2014.
He hasn't enjoyed the best of starts at the Bavarian giants and he was withdrawn at half-time during the 3-0 defeat to Paris Saint-Germain in the Champions League, which turned out to be Ancelotti's final game in charge.
He then watched on from the bench during the German champions' 2-2 draw against Hertha Berlin and the 26-year-old reportedly fears he will not get enough playing time now Ancelotti has left.
According to Spanish publication 'Diario Gol', Rodriguez, who won the Golden Boot at the 2014 World Cup, is struggling to settle down in Germany and is not enjoying the colder weather. His inability to communicate with team-mates in the native language is also proving a problem for the man on-loan from Real Madrid.
Although Rodriguez reportedly favours a move back to Real Madrid, he is unlikely to find himself welcome in the Spanish capital and any break in his two-year loan agreement at Bayern would likely see him leave Los Blancos permanently next year.
Zidane was never convinced by Rodriguez and allowed him to leave in the summer so Marco Asensio, who has since emerged as one of Europe's most promising talents, could benefit from more game time.
Real Madrid president Florentino Perez will be hoping to recoup as much of the £71m he splashed out on Rodriguez after his outstanding performances at the World Cup in Brazil.