WS has held the account for four years and is expected to repitch for the work.
The pitch is part of a review of Virgin Media's public affairs management.
The news comes as the broadband and TV group pushes ahead with plans to take a secondary listing in the UK in an effort to raise its domestic profile and attract more investors.
The public affairs brief includes government and opposition liaison and regulatory affairs.
Virgin Media's director of corporate affairs and media Paul Richmond is leading the pitch. It is believed to be in its early stages, with an agency expected to be appointed by the end of the year.
Virgin Media brought in Bray Leino in May to handle its nationwide regional media relations account, under head of corporate and consumer PR Michelle Gordon.