The billionaire, who also owns OK! magazine and various adult TV channels via his Portland business, is believed to have reached the final stages in the Five auction, which is being run by US investment bank JP Morgan.
While Desmond has never publicly confirmed his interest in the loss-making Five, he did say in a recent BBC Radio 4 interview that he wants to be involved in the expected consolidation in the media industry.
Desmond, who according to The Sunday Times Rich List has a personal fortune of £950m, has also openly discussed his substantial cash pile for acquisitions.
Last month, he said in an interview: "I've got so much money, it's ridiculous. I know exactly what I want and exactly what I'm going to do."
JP Morgan is also believed to have received expressions of interest in Five from Sky, Time Warner, NBC, Endemol and a consortium involving Greek broadcaster Antenna and Big Brother creator John De Mol.
However, ITV and Channel 4 are no longer thought to be in the running to acquire Five, which is home to Neighbours and CSI.
The commercial broadcaster is thought to have performed better this year than it did in 2009, when it reported a loss of £37m leading to RTL writing down its value from £500m in 2007 to just £112m last year.
However, investment analysts believe that a deal for Five could be worth up to £300m due to its terrestrial licence and several valuable slots of the Freeview platform.
Over the next month, JP Morgan will narrow down the bidders to just two main suitors. Negotiations will continue over the remainder of 2010, with the sale likely to be concluded during the first quarter of next year.