The Blues are currently looking for a new boss following the recent sacking of Lee Clark.
Dons chairman Pete Winkelman has been quick to reject Birmingham's approach to speak with Robinson, something that the 34-year-old has taken as a compliment.
"I'm flattered - but just as flattered by the chairman's response. It shows he wants me at this football club," he told BBC Sport. "That gives me the satisfaction of knowing you're wanted somewhere.
"To be linked to a club like Birmingham City - it's a massive football club in one of the biggest cities in the UK. People talk about my name being in for this or that - it's nothing to do with me. The fact that people go to the chairman means I have to answer these questions."
Robinson joined MK Dons in 2010, making him the fourth longest-serving manager in both the Premier League and Football League.