The mobile phone network is looking for ways to rejuvenate its DM strategy.
The account, which is held by Tequila\London, has lain dormant since the end of last year.
3 has approached a number of agencies about a brief to develop an acquisition strategy using DM and digital to increase its customer base.
The network has previously relied on cut-price text and voice packages to drive customer growth. This has drawn three million UK customers to the network, which reported in April that it lost £4.7 million a day last year.
The brand is in the process of holding credentials meetings with a view to drawing up a shortlist of agencies.
The network's last direct agency was TBWA\GGT, which merged with its sister agency to become Tequila\ London in January.
TBWA\GGT continued to work on the business after its above-the-line sibling TBWA\ London lost the 3 ad account to WCRS in May last year. However, sources say 3 called a halt to its below-the-line activity at the end of 2004.
TBWA\GGT originally won the business in August 2002 from the Communications Agency, after landing the interactive advertising account in a pitch five months earlier.
No-one from 3 was available to comment.