Soon after the end of the season, it was claimed that Downing was not part of Garry Monk's plans at the Riverside Stadium and that he was free to find another club.
The 32-year-old will not be short of offers this summer and according to the Birmingham Mail, the Blues have made their move to take the versatile player to the West Midlands.
It has been suggested that discussions will take place at the start of next week, with Harry Redknapp looking to add another experienced name to his squad at St Andrew's.
Downing made 34 appearances in all competitions last season, but he was unable to prevent Boro from returning to the Championship at the first time of asking.
Birmingham have already made a statement in the transfer market, with David Stockdale, Marc Roberts and Craig Gardner all completing transfers to a team who only remained at the second tier on the final day of last season.