The global electronics giant is believed to be talking to pitch consultants with a view to inviting a list of agencies to present in the new year, after the important Christmas sales period has passed.
A review of the account would represent a major blow for TBWA\London, which has held the account for more than ten years.
The agency has been responsible for a series of iconic campaigns, and has won a number of awards, including the Grand Prix at Cannes in 2004 for its "mountain" spot. Sony Computer Entertainment won Advertiser of the Year at Cannes in 2005.
Sony Computer Entertainment America told TBWA\Chiat\Day in July that it was putting its $150 million US account up for pitch.
In the past year, TBWA\London has been hit by the departure of several key members of the PlayStation team.
The joint-creative director Tony McTear, the man behind the "mountain" film, left the agency in June. He has since joined Fallon.
Other figures to leave include Alex Best, who is joining Fallon as the group account director on Cadbury and Budweiser, and the executive planning director, Neil Hourston, who is going to Grey.
Sony has been beset by problems since the launch of the PlayStation 3, which was delayed by a series of technical problems to March this year.
Since then, the Nintendo Wii and the Microsoft Xbox 360 have been outselling the PS3. Sony cut the price last month to increase sales after complaints it was too pricey.