The Rams are said to be eyeing 22-year-old Robinson after seeing an offer for Leicester City's Tom Lawrence turned down.
Their interest in Robinson has not reached the bidding stage.
Robinson netted 11 goals last season, 10 of those in the Championship and the other against Arsenal in the FA Cup.
He played up front and on the left-wing last term, and during pre-season under Alex Neil has operated both on the left flank and in the No.10 role.
Robinson is the second Preston player to attract interest from a Championship rival this summer, North End having turned down a £2.5m bid from Birmingham City for Jordan Hugill last month.
PNE open their Championship campaign against Sheffield Wednesday at Deepdale on Saturday afternoon.
They face Derby at Pride Park on Tuesday, August 15.