Sony picked up the rights to make a film of Jobs's life after the acclaimed technology leader died of pancreatic cancer last month at the age of 56.
Aaron Sorkin, the Oscar-winning screenwriter of The Social Network, is understood to have been contacted to adapt the script from Walter Isaacson's biography of Jobs.
Filming for the biopic is scheduled to get underway next year.
Clooney, 50, is said to be up against 40-year-old Wyle to play Jobs, after the two starred opposite each other in the long-running US drama ER.
However, Wyle may have the edge because he previously played the former Apple chief executive in the 1999 cult classic TV movie Pirates of Silicon Valley.
To research the film, which documented the rivalry between Jobs's Apple and Bill Gates's Microsoft, the actor was invited by Jobs to that year's Macworld Expo, after which the pair went to dinner.
Recalling the meeting, Wyle told Fortune magazine: "He (Jobs) took his napkin and started sketching out the schematics and he passed the napkin around the table. The cheque soon came and we started to get up the leave - and the napkin just sat there on the table.
'I thought to myself, 'I got to take that napkin', and my hand was on it, but Steve called from the door and asked, 'Noah, you want to share a cab with me?' So I put the napkin down. I could have had an Edison original."
Whoever secures the chance to play Jobs will have to portray one of the most enigmatic and indeed quotable people ever to work in the technology industry.
Watch Steve Jobs give a landmark speech to graduates of Stanford University in 2005 below:
See pictures of Steve Jobs's biggest moments below: