The club have come out and said though that he will not be moving on.
Club chief executive Sam Rush said, according to BBC Sport: "There is no question whatsoever of him leaving.
"He is one of the highest-performing managers in English football, so he is going to be linked and admired by others. But we have had no approaches."
Importantly, Rush insists McClaren has reiterated his commitment to Derby.
"I'm aware that there is speculation about Steve at the moment but he has completely dismissed it. His future is with us," Rush said.
Derby who are in the top six of the Championship progressed to the fourth round of the FA Cup on Saturday after a late penalty gave them a 1-0 win over non-league Southport.