City boss Roberto Mancini is set to strengthen his attack in the summer following Mario Balotelli's January exit.
The club didn't sign a replacement for Balotelli and there has been speculation that both Carlos Tevez and Edin Dzeko could be on the move at the end of the campaign.
Gomez has fallen behind Mario Mandzukic in the pecking order at the Allianz Arena and is expected to be sold by incoming Bayern boss Pep Guardiola as the Spanish boss seeks to reshape the squad in Munich.
City have been tentatively linked with a move for the 27-year-old German international, although a number of forwards have been mooted as possible City targets following Balotelli's exit, including Atletico Madrid star Radamel Falcao and Napoli's Edinson Cavani.
Gomez would represent a cheaper option that either Cavani or Falcao, as their respective clubs are keen to keep hold, but the German international will still command a hefty fee due to his impressive goal scoring record in the Bundesliga.
Gomez has 67 goals in 103 league appearances for Bayern and averaged a goal every two games for previous side Stuttgart, with whom he spent six years before moving to the Allianz Arena in 2009.