Ex-England international Green, who was capped 12 times for his country, was recently released by Huddersfield Town after failing to make a single appearance since joining from Leeds United last summer.
The 38-year-old may be in the twilight stage of his career but interest in the shot-stopper is still said to be high, with Birmingham believed to be readying a contract offer.
Having narrowly escaped Championship relegation this past season, the Blues are eager to invest in the squad wisely and manager Garry Monk is hopeful of bringing in some experienced heads.
If Green were to make the move to St Andrew's it would see the keeper reunited with Monk after the duo worked together at Elland Road.
Birmingham are worried over the futures of both David Stockdale and Tomasz Kuszczak with reports claiming the duo are attracting interest from elsewhere, and the addition of free agent Green would represent good value for money.
Toby Alderweireld believes Tottenham fans should be proud that the club had so many representatives at the World Cup.
Roy Hodgson says Crystal Palace are 'not a selling club' and have no intention of selling Andros Townsend or Wilfried Zaha.