The 18-year-old England under-21 international is already an established part of the Championship side's starting eleven, and Liverpool were strongly tipped to be considering a January bid.
But the report claims Everton are now set to rival their Merseyside neighbours with an offer of their own when the winter window opens.
Toffees boss Roberto Martinez travelled with two club scouts to check out the teenage playmaker first-hand as Derby earned a 2-2 draw against Bolton at the Reebok Stadium.
Liverpool manager Brendan Rodgers has been a long-term admirer of Hughes, and reportedly identified him as a future target over the summer.
And a separate report in the Daily Mirror claims the Reds chief dispatched a scout of his own, Dave Fallows, to watch Hughes in action in the same game.
The 18-year-old, who has drawn comparisons with Liverpool legend Steven Gerrard, provided an assist before a hip injury forced an early exit.
But Derby will refuse to entertain offers on the cheap. The Daily Express quotes Derby boss Nigel Clough as saying last month: "Would it be more than £6m? Yes, I think it is fair to say that.
"We just think it is going to be a very, very substantial figure to tempt him away."
A fee in the region of £10m has been mentioned, but it's unclear whether either Liverpool or Everton are willing to pay such a figure.