The Burnley-based Time has shortlisted McCann-Erickson and Lowe Broadway to pitch for the business alongside Poulter Partners in Leeds, Manchester's BDH/TBWA and Coltas in Glasgow.
The assignment is being presented to agencies as a one-off project, although industry sources believe an appointment may lead to a permanent relationship.
A decision is expected by next week.
BDH handled Time's £26 million account before it moved to HHCL & Partners two years ago. The client currently produces its creative work in-house.
Poulters, which previously pitched against BDH for the Time account, is believed to have made the list because of its extensive retail experience gained in handling the Morrisons supermarket chain.
Time is said to be eager to promote its new retail operation with a national TV campaign. However, its £5 million budget will leave it outgunned by the Dixons-owned PC World, which spends more than £25 million a year through M&C Saatchi and Walker Media.
Brian Trevaskiss, the Time group marketing manager, was unavailable for comment as Campaign went to press.