The organisation has begun a process through the Crown Commercial Service. It currently works with Abbott Mead Vickers BBDO.
AMV won the business in November 2014 after a pitch. Before AMV, Leagas Delaney had handled the account since 2011.
Rapp oversees CRM and data planning for The Open University. MediaCom handles the media business.
A spokesman for the organisation said: "AMV was appointed at the time when TV advertising formed the main thrust of The Open University’s strategy and it successfully established ‘life-changing learning’ as our core emotional driver. We are now moving to a much greater digitally driven and relationship-managed strategy."