International architects are being invited to submit proposals for the brownfield site bordering the M1 which can either incorporate or exclude the infamous towers.
Public interest in the towers - now almost 70 years old - was fired up recently when they became the focus of Channel 4's Big Art programme.
In a statement the RIBA says: 'People either loathe the towers, considering them an eyesore, or love them, regarding them as a local landmark that welcomes residents and visitors alike to Sheffield.
'Despite its industrial setting, the site is significant as the River Don and Tinsley Canal, which cross the site, are an important recreational resource and wildlife corridor that links to the adjacent Blackburn Meadows nature reserve.'
The competition is being staged on behalf of Groundwork Sheffield and up to twenty schemes will go on show at a public exhibition.
Cash prizes will be awarded to the winner and two runners-up. For further details contact the RIBA competitions office on 0113 234 1335 or visit www.riba.org/go/RIBA/Also/Competitions_2027.html .