Black Cats boss Steve Bruce is keen to bolster his options in the middle of the park following Jordan Henderson's big-money exit to Liverpool.
Sunderland are believed to be weighing up a £5million offer for the talented schemer, although Blues will be holding out for the best possible price for the 24-year-old.
Gardner was the club's leading scorer last season with 10 goals in all competitions, but he is expected to move on this summer as Birmingham look to offset the cost of relegation.
The Black Cats, however, face competition from North-East rivals Newcastle as Alan Pardew's troops are also hoping to raid St Andrew's.
It has been a turbulent start to the week for Birmingham with manager Alex McLeish tendering his resignation over the weekend with rivals Aston Villa mooted as possible suitors.