3 has held discussions with several agencies including WCRS but intends to invite a range of advertising agencies to pitch for the account.
TBWA will be asked to repitch for the business. However, 3 has indicated that if a new brand campaign, due to launch shortly, proves to be successful, the full review might be called off.
However, an insider at 3 said that the time was right to look at reviewing the business, as TBWA was nearing the end of its second year in contract.
But a company spokesman said: "TBWA is our above-the-line agency and we are happy with the work it is doing and are not conducting a review at this time."
3 has struggled to attract customers since its much-delayed launch in March, with TBWA's multimillion-pound campaign failing to capture the imagination of the public.
The company has reportedly achieved sales of just 25,000 phones in its first three months of retail operation. The price of more than £200 for its phones and costly airtime packages have proved a major turn-off to customers.
Last month, 3 restructured its senior management team. The strategy and marketing director, Lisa Gernon, invoked a clause in her contract to revert to her initial position as a consultant. Gareth Jones, a former Orange executive, was hired as the chief operating officer. Graeme Oxby was then installed as the interim marketing manager.
The managing director, Colin Tucker, became the deputy chairman and joint chief executive and Bob Fuller, the chief executive of 3 in Italy, took over the daily running of the UK company.
As part of the drive to combat slow sales, 3 recently appointed Susan Branchflower to the new role of head of segment marketing to spearhead 3's consumer pricing propositions and promotions.
The advertising review is a part of a wider operational review that 3 has kicked off.
In November, the TBWA managing partner on the 3 account, Gavin Thompson, resigned, and was replaced by Katie Halling, Abbott Mead Vickers BBDO's senior group account director. However, Matt Shepherd-Smith, the agency's joint managing director, now runs the account.
In April, Hutchison decided to run a selection of brand-awareness TV commercials produced by its below-the-line agency, TBWA/GGT.