Stewart could be next out of Dens Park, with Gary Rowett's team said to be circling.
Top scorer Kane Hemmings departed for Oxford United in a £250,000 deal on Wednesday and his strike partner could be next it seems.
Stewart, who was previously linked with moves to Leeds United and boyhood club Rangers this summer, has less than a year to run on his contract at Dens Park.
As such, the report claims Birmingham's bid will also be around the quarter-of-a-million-pound mark.
Stewart, who can play on either flank as well as up front, has scored four goals in two League Cup appearances so far, having scored 11 times in all competitions last term.
The 26-year-old told the Dundee Evening Telegraph earlier this month: "I want to be somewhere I can play my best football. Whether it is at Dundee we will just have to wait and see.
"I have ambitions, just like most people. I want to play at the highest level I possibly can."
Birmingham are expected to add to their ranks in the coming weeks, after seeing a host of players depart and only four new signings arriving - three of whom were on loan at St. Andrew's last term.
The Sun reported on Thursday that the Blues are keen on Spanish forward Juan Villar and Uruguayan defender Leandro Cabrera, who both play in Spain's second tier.