Middlesbrough, who have been linked to the player by the Mail, have been the favourite in the market for some time. However, the Rams have leapfrogged Boro into pole position and are now at much shorter odds than their competitors.
Derby are priced at 5/2 to land the Scotland international, while Middlesbrough 4/1, Crystal Palace 6/1 and Sheffield Wednesday 8/1, all join Derby in filling the top four.
Do Derby County need to sign Rhodes?
After adding Andreas Weimann and Darren Bent to their attack, the Rams already have one of the most impressive frontlines in the division.
Rhodes, who has scored more than 20 goals in each of the last six seasons, would be an excellent addition to an already impressive Derby side. However, the money that would need to be spent could be better spent elsewhere.
Last season, goals were not the problem for the East Midlands side as their defensive errors ultimately ensured they would be condemned to another year of Championship football after a very promising start.
Nevertheless, if Derby were to sell Chris Martin this summer then their interest in the forward could accelerate as they would need to replace their influential frontman ahead of the new season.
Until then, it seems unlikely any deal regarding Rhodes to Derby will happen.