The Teesside club want the 25-year-old to spearhead their Sky Bet Championship promotion charge next season and are willing to offer Rovers a profit on the £8million they paid Huddersfield three summers ago.
With Blackburn currently still under the constraints of a transfer embargo , Rhodes believes Aitor Karanka's Boro, beaten play-off finalists in the Championship in May, represent a step up
The east Lancashire club rejected Hull's £12million advances for the player last summer but, despite the fact Rhodes remains under contract for a further four years, his decision to publicly indulge Boro could help force through a move
"I have been advised by the club that they have rejected an offer from Middlesbrough for my services which was in excess of what Blackburn paid for me," Rhodes told ESPN FC.
"I am ambitious and have never hidden my desire to play at the highest level possible and that was one of the reasons why I left Huddersfield Town for Blackburn.
"When I left Huddersfield I felt the timing was right in the next stage of my career and, having seen Middlesbrough's performances last season in reaching the play-off final and their ambition this summer in terms of acquisitions, I would have liked to have been able to talk to them and I am unhappy at not being given that opportunity."
Blackburn's owners Venky's have previously adopted a hard-line stance on offloading Rhodes and he has kept his counsel on a possible move away.
Boss Gary Bowyer praised him when he scored against Bournemouth and Bolton last term in the immediate aftermath of transfer speculation but, having now stated his desire to leave Ewood Park, Venky's may find their hand forced.
Source : PA
Source: PA