The council, which became Tory in 2005, paid the London firm nearly £300,000 before it decided to drop the project.
The revelation came after a Freedom of Information Act request by The AJ.
The council, which was Labour-controlled when it backed the project, has since decided to proceed with a 'split site' solution.
Rogers' final architectural bill was divided between £120,000 for work on the 2003 concept and £160k for space planning designs carried out around the scheme in 2003 and 2004.
The designs - which formed the centrepiece to the Eastside regeneration initiative - were dropped in 2005 when the Conservative Party wrested control of the council back from Labour.
Following a consultation and research exercise, the new Tory leadership then announced that it did not consider the library good value for money.
Both political parties have constantly bickered about the actual cost of the project, with former council leader Albert Bore claiming that the 'split site' solution could cost more than Labour's plan.
Bore has previously claimed that he would resuscitate the Rogers plans if he were to win back power.