The source claims that Apple will launch the service on 15 January, and that titles will rent for US$3.99 for 24 hours.
The company is reported to be already signing up movie studios for the deal.
"Once a couple of studios do it, how long can the others resist?" Richard Greenfield, an analyst at Pali Capital, said in an interview with Bloomberg. "It becomes only a matter of minutes before the others come on board too."
Other reports have cited 20th Century Fox as signing up to the iTunes service.
Apple chief executive Steve Jobs is expected to provide more details at the in San Francisco next week.
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iTnews Executive Retreat - Security Leaders Edition
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