Borkowski PR and a local agency are believed to be among those invited to pitch.
MWPR managing director Rita Rowe will head the account, reporting to Green King marketing director Susan Thomas-Taylor.
Rowe will also report to Greene King's new MD, Rooney Anand, who ordered a review of PR and communications strategy as part of a restructure of the brewery.
'We expect to be very busy as the various brands come under review and are then given a relaunch,' said Rowe, who will lead a four-strong team from MWPR's London and Manchester offices.
Greene King produces fine ale brands, including IPA, Old Speckled Hen and Abbots Ale.
Rowe said her team would work closely with Greene King's four-strong PR team.
'We are putting together a campaign of integrated communication to reposition each of the brands and make them more relevant in their target markets,' she added.
The first ad campaign saw the relaunch of Abbots Ale via poster sites, and was followed by a TV campaign for IPA, which attempted to position the brand as 'young, fun, cheeky and tempted'.
The appointment comes as MWPR itself undergoes a restructuring and rebrand, which will see it emerge as part of new organisation called MUSE.
It will have offices in London, Manchester, Hitchin in Hertfordshire and Calgary, Canada.