The entertainment business, which is owned by News Corporation, has held preliminary talks with agencies about moving the media account out of incumbent Starcom UK.
20th Century Fox is the biggest division of News Corporation, generating $5.9bn (£3.4bn) in revenue and $1.1bn in profit in the year to 30 June.
The company's UK operation is split between the 20th Century Fox Home Entertainment division, which distributes DVDs and videos, and 20th Century Fox Films, which distributes movies to cinemas.
'Star Wars: Episode III - Revenge of the Sith', was one of Fox's biggest releases of the year, backed by an advertising budget of more than £2m.
The film industry has been hit by falling cinema attendances. In the US, audiences have fallen 10% year on year, while in the UK they slipped from 176m in 2002 to an estimated 170m this year.
Current cinema releases from 20th Century Fox include 'In Her Shoes', starring Cameron Diaz, and 'Transporter 2', starring Jason Statham. No one at Fox would comment on its media plans.
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