Rhodes plundered a stunning 40 goals last term to help the Terriers to promotion, with a host of clubs in the market to sign him.
Fulham remain big admirers of the 22-year-old, one of the hottest properties in the Football League.
Blackburn’s need for a striker has been heightened by a cruciate knee ligament injury sustained by £3m summer signing Leon Best, with Rhodes their no.1 striking target.
Initial interest in Rhodes is believed to have been rebuffed, but with funds available, Rovers are refusing to give up in their pursuit of Rhodes.
Meanwhile, Robert Koren’s agent has revealed that the midfielder is close to agreeing a new deal with Hull City.
Koren, 31, has a £500,000 buy-out clause in his current contract, with Nigel Pearson’s Leicester City have made such an offer.
But the Tigers have offered a contract extension to Koren, taking him to the end of the 2014 campaign and a deal is said to be close.
Koren’s agent Sam Stapleton said: “We are close to agreeing a new contract with Hull and Robbie is keen to try to wrap it up this week as he wants to concentrate on the season in front of him.”
Veteran Sheffield Wednesday striker Ryan Lowe has completed his move to MK Dons on a two-year-deal with the Owls thought to have recouped the majority of the £100,000 they paid out to sign him last August.
Sheffield United boss Danny Wilson is being linked with a move for Blackburn striker Nick Blackman, 22.
Bradford City boss Phil Parkinson is sweating over the fitness of midfielder Ricky Ravenhill, who limped off with a knee injury in last night’s 4-0 friendly win at Guiseley.
Bermudan striker Nakhi Wells struck twice for the Bantams, with midfielders Gary Jones and Ritchie Jones also on target.