Sources in Germany say City boss Sven Goran Eriksson's assistant Tord Grip travelled to Bavaria last week to check on the player and he was receptive to a move to the Barclays Premier League, says the Daily Mail.
The 22-year-old Germany forward has fallen out with officials at the club and is available for around £12million.
City, who have also considered a loan deal, remain wary that Jurgen Klinsmann's appointment to take over as manager next season could yet affect any transfer.
Podolski said: "The way it works here is you score a couple of great goals, then you only get 45 minutes next game, then you're dropped for three. That's not good enough for me.
"I want to prove myself here but I don't want to go grey on the bench."