It has issued a tender document to interested agencies, inviting them to pitch for the account.
This follows a similar process for the advertising account, which is held by Start and kicked off in April.
MG OMD, which plans to re-tender for the business, was appointed following a pitch in 2005 and has worked on a range of activity for the Royal Mint, focusing on national newspapers and magazines.
Products supported by media activity have included the Mint's collector coins range and the launch of its £5 coin.
In addition, the agency has developed direct response campaigns to drive traffic to the Royal Mint's retail and corporate websites.
Royal Mint has yet to hire an advertising agency and is conducting that review by electronic auction. It expects to have an agency in place by August.