The charity has opened discussions with Abbott Mead Vickers BBDO, Archibald Ingall Stretton and Draft London about the business.
AMV is said to be already working on a project for the charity, although the pitch is specifically for a DM brief.
EHS Brann, which is not repitching, won the account in June last year from WWAV Rapp Collins, which held the business for 11 years.
The split with EHS Brann came amid internal disagreements within Oxfam about the future direction of its fundraising efforts.
Edward Fox, Oxfam's director of fundraising, said: "This in no way reflects on the work that EHS Brann has completed for us.
"We are very pleased with the work it has done, but we have come to a crossroads and mutually agreed to pursue other opportunities."