Haystack has yet to compile an agency shortlist, but aims to hold pitches over the next few weeks with a view to making a decision at the end of the month.
First Quench refused to comment on whether C&W would be involved in the repitch.
The move forms part of a group-wide review of PR, sparked off by the appointment of sales and marketing director Kevin Stiles, formerly Thomas Cook marketing director, who joined early last month.
First Quench head of PR and own brand marketing Helen Munday said: 'With his (Stiles) arrival, he wanted to make sure that we've got the right roster of agencies matching the company's needs and we are undertaking an evaluation of agencies we work with and other agencies.'
Munday said corporate PR remained unaffected and the company would continue to retain Financial Dynamics.
FD was hired alongside C&W following a communications overhaul last October in the wake of First Quench's sale to Nomura International.
Last year's review saw external PR, previously overseen by Communique PR, split between FD and C&W for corporate and consumer work respectively.
Munday said it was likely the consumer brief would remain with one agency rather than a network of consultancies hired for individual brands.
Comms chief Stiles replaces Paul Vines, who was brought in on an interim basis to fill the vacancy left by the departure of Ralph Hayward 18 months ago.