Blues boss Lee Clark is keen to bolster his attacking options this summer and has identified Green as somebody he wants to look at more closely.
The 26-year-old has scored 57 goals in the past two seasons and has helped the Stags clinch promotion back to the Premier League, so Mansfield boss Paul Cox is not keen to let him go.
"I am planning for the worst-case scenario," Cox said in the Birmingham Mail.
"He's been on trial at Birmingham for a week or so, but nothing has happened there for him yet so we are still hopeful.
"I would love to work with Matt next season - I love the kid to bits. But he has a family to look after and I am sure he will give his decision a lot of thought.
"If he does go to a bigger club, we are pleased we have had a say in it."