Mindshare is the incumbent and is not pitching. The shop picked up the business from OMD in 2012 when it was reported to be worth £12 million.
The Post Office has shortlisted agencies ahead of pitches this week. RFIs were issued at the beginning of the year.
The process is being run through the Crown Commercial Service and the Post Office is looking to make an appointment in May.
Pete Markey, the chief marketing officer, and Keith Gulliver, the head of marketing communications, are leading the review.
MullenLowe London handles the Post Office’s creative account. It picked up the business in November 2014, when it was known as DLKW Lowe. The shop beat Ogilvy & Mather and WCRS after a seven-month process.
In November last year, the Post Office released its second ad featuring Simon Bird, who starred in the Channel 4 show The Inbetweeners.
A Post Office spokeswoman said: "In line with the public procurement policies we follow, we have reached the stage where we have to repitch our media agency relationships."