Robson has enjoyed some fine form at Tannadice this season

The Turf Moor club are thought to have made a bid of �750,000, with an additional �200,000 to be paid if they won promotion to the Premier League.

The Tannadice outfit turned that down, along with a lesser offer from League One side Nottingham Forest.

Chairman Eddie Thompson said that neither club had matched his valuation of the 29-year-old midfielder.

Birmingham had earlier made an inquiry about the player, who has also been linked with Newcastle and Celtic.

Robson has been at Tannadice since joining from Inverness Caledonian Thistle for �50,000 in 2003.

But he has blossomed under manager Craig Levein and won his first international cap, in an August friendly against South Africa.

In the last year, he has really got a grip on what he is doing on the field and off it Dundee United manager Craig Levein

And his stock will have risen further after his winning goal against Clyde in the Scottish Cup last midweek and two more on Saturday against Aberdeen.

Thompson had warned last month that Robson would not be allowed to leave Tannadice on the cheap and promised to be difficult to deal with.

But this week the chairman admitted: "There's a whole stack of people watching him.

"But Craig and I want to keep him. You saw the way he struck the ball in from 35 yards the other night, passed the ball into the net on Saturday then you knew where he was going to put that free-kick."

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And Levein told BBC Sport: "Barry Robson is a 29-year-old man with a couple of kids who, in my opinion, has only really blossomed in the last year or so.

"He's always had talent, but his consistency was nowhere near what it should have been.

"In the last year, he has really got a grip on what he is doing on the field and off it.

"He is working hard and playing well and that is always going to attract interest from other clubs."