The 33-year-old recently revealed on his blog that he would not tour again for the foreseeable future and would not produce a new album this year.
EMI, owned by Terra Firma, has already seen acts including Paul McCartney and Radiohead leave amid criticism of its methods, and the defections underline radical changes in the music industry due to the Internet.
Industry insiders questioned whether Williams's threat could be a negotiating tactic as both sides discuss an advance and marketing budget for any new album, but they also noted it is rare for such disputes to appear in public.
As a company new to the music industry, it is also not clear how Terra Firma will react.
"The question is, 'should Robbie deliver the new album he is due to release to EMI?' We have to say the answer is 'no'," Williams' manager Tim Clark was quoted as saying by the Times on Friday.
"We have no idea how EMI will market and promote the album. They do not have anyone in the digital sphere capable of doing the job required. All we know is they are going to decimate their staff," he added.
"EMI can sue or pay up his contract. Robbie needs to know what services EMI can provide to an artist of his standing."
SOLO CAREER
Clark, his ie:music group and EMI were all unavailable for immediate comment. The British music group is expected to outline restructuring plans next week.
Williams has sold more than 50 million albums and forged a successful solo career since leaving boyband Take That. He moved to EMI in 2002 in a reported 80 million pound ($156.5 million) deal, although his recent sales have been disappointing.
According to the Times, another of the label's biggest acts, Coldplay, is unhappy after EMI's head of music in Britain, Tony Wadsworth, left this week.
Wadsworth had spent 26 years at EMI and was behind several of EMI's most successful signings including Radiohead, Blur and Supergrass. Part of Wadsworth's responsibilities have been taken over by Mike Clasper, a former chief executive of airport operator BAA.
Guy Hands, head of Terra Firma which bought EMI last year for 2.4 billion pounds, has warned artists they would be dropped if they did not work hard enough for the group and called for a "fundamental shift" in the way the company did business.
He told reporters recently he loved to find the worst performing businesses in the most challenged sectors "and we get really happy if it's really, really bad."
Record companies are struggling to make up for declining CD sales and the illegal downloading of music over the Internet.
Although legal downloads are growing fast, it is not enough to make up the shortfall, and artists are increasingly turning to touring, merchandise and online innovations to make money.
Radiohead released their new album "In Rainbows" over the Internet last year, allowing fans to pay whatever they wanted to download it.
(Reporting by Mike Collett-White and Kate Holton; Editing by David Holmes)
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