Bruce, however, has rubbished the reports and hinted strongly that he will not be selling any of his players this month as he seeks an immediate return to the top-flight.
"As far as I am concerned I don't know where that's come from. Would I really contemplate selling him to Derby? I don't think so,” Bruce explained.
"He's a smashing young player, who is still learning his trade, but I can't see us wanting to sell one of our better players to Derby.”
"I can certainly quash that one. Even if they got to double that figure I don't think we would be selling - why would we want to break anything up now?
"We want to try and improve the squad if we can, not disband it."
Hull currently occupy second place in the Championship table, one point ahead of Derby as the two appear the most likely to battle for an automatic promotion spot alongside Middlesbrough.
The Rams are short on left-backs following the long-term injury to Craig Forsyth, and following the addition of two forwards in January their attentions may have turned to strengthening this area.
Robertson is widely regarded as one of the league’s outstanding fullbacks, and for Hull to sell him to a promotion rival at this stage of the season would be rather nonsensical.