The German international has been the stand-out performer for both his club and national team in recent seasons and have reportedly been linked with moves to Liverpool and Tottenham Hotspur.
Marin is widely tipped as a future star in European football and is expected to join a top club in the near future.
That could now happen this summer as City have indicated their interest in signing the 22-year-old as they look to launch a double assault on the Barclays Premier League and Champions League.
The former Borussia Mönchengladbach player is believed to be keen on staying in Germany, but could find the lure of Champions League football and high wages hard to resist.
"If the club receives an offer and decides to sell me, that is another situation. Until then I am happy here," Marin told German newspaper Bild.
Marin joined Bremen from Mönchengladbach in 2009 for €8.5 million.