City manager Roberto Mancini has moved quickly after losing England international winger Adam Johnson or three months with ankle ligament damage.
Swede Larsson, 25, is out of contract at St Andrew's in the summer.
City switch: Midfielder Larsson is set to swap Birmingham for Manchester
Larsson joined Arsenal as a 16-year-old in 2001 and made his debut - against Manchester City - in 2004.
He initially went on a season-long loan to Birmingham in August 2006 and a permanent switch was agreed at the end of that campaign.
Aston Villa, Blackburn and Newcastle have all been linked with Larsson this month.
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