The broadcaster wants to run a live TV head-to-head featuring existing FIFA president Sepp Blatter and challenger Mohamed Bin Hammam on the eve of the June 1 election.
John Ryley, the head of Sky News, has written to Blatter and Bin Hammam asking them to take part in the debate. Bin Hammam has accepted the offer, but Blatter has yet to respond.
Ryley, who played an integral role in getting the prime ministerial debates introduced for last year's UK general election, said that the race for the FIFA presidency will "help decide the future path of the game and its importance cannot be underestimated".
Among the key issues under scrutiny is the how greater transparency would be introduced within world football governance, following recent allegations of corruption.
An online petition has been launched for the campaign and various public figures and organisations have already lent their support, including the 180,000-member Football Supporters' Federation.
FSF chairman Malcolm Clarke told Sky News: "The Football Supporters' Federation supports anything that can increase transparency in this election to let football supporters know where each of the candidates stand. There is no more important post in football."
Prime minister David Cameron, who took part in the UK leaders' debates last year, has also given his support for the plans. His spokesman said: "Anything that allows the candidates to set out their views and plans to the football watching public would be a good thing."
Sports minister Hugh Robertson added: "It's a fantastic idea for the two candidates to have a live television debate. This would give them an opportunity to convey their plans to the football-loving public and highlight how they might look to reform the organisation and make it more transparent."
Lord Sebastian Coe, mayor of London Boris Johnson, Conservative MP Louise Bagshawe and Football Association chairman David Bernstein have also backed the move.
Blatter and Bin Hammam are currently on the election trail, attempting to gain support from the 208 football associations around the world ahead of the crucial vote.