The 20-year-old is currently on loan at League One side MK Dons where he has netted 16 goals in 28 appearances so far this season.
Bamford's fine form saw him make his England Under-21 debut as a substitute in November's 9-0 thrashing of San Marino, resulting in a host of Championship clubs, including Wigan, Burnley and Middlesbrough being linked with his services.
Bamford briefly worked with Rams manager Steve McClaren during his time at Nottingham Forest, who he left for Chelsea in 2012, signing a five-year deal at Stamford Bridge.
The former England boss is believed to be a keen admirer of the striker and he admitted that Bamford would meet the criteria for any potential January signings.
"What we have done is we have gone for younger players, the likes of Andre Wisdom and Michael Keane, and even Simon Dawkins, who I keep thinking is only 18 or 19, and he is 26," he told the Derby Telegraph.
"So, we have gone for younger players from the top teams and we want that quality.
"We are looking for youngsters again to add to the squad and improve the quality we have got."
Bamford's current manager, Karl Robinson at MK Dons, conceded it would be unlikely that he would be able to keep hold of the youngster beyond his current deal which expires on January 5.
"We'll speak to Chelsea but I'll be surprised if he is still with us in January," he said.
"He's a special talent and has scored a number of goals. He is someone who is going to go from strength to strength."