More than three City PR agencies - including Fishburn Hedges and GCI Financial - are understood to be shortlisted for the pitch.
There is no incumbent currently handling the brief, although O'Keeffe said consumer agency The Red Consultancy recently provided some ad hoc advice.
GCI also previously worked on the personal finance brief for a number of years.
'We're looking at media relations work and want to get someone on board as quickly as possible,' said O'Keeffe.
O'Keeffe recently took on the role of head of group and retail PR, promoted from her former post as head of group PR.
She replaces Louise Footner, following her departure to Surrey County Council as head of communications after eight years with the high street bank (PRWeek, 21 June).
Footner succeeded Mark Oakes, who left Surrey in April to join social care watchdog the General Social Care Council as director of corporate communications.
She took maternity leave in March and Barclays regional communications director David Blake acted as interim head of the bank's retail PR prior to O'Keeffe's promotion.
The role has since been expanded to cover O'Keeffe's original group PR remit alongside the retail brief.
The Barclays personal finance business up for grabs is said to focus on all personal finance products, including the bank's Open Plan product.
Barclays bought the Woolwich building society in 2000, adding the internet operation Open Plan to its mortgage offerings and increasing its retail customer base to 16 million, while doubling its mortgage market-share.
Other products covered are believed to include pensions, savings and ISAs, insurance, credit cards and loans.