The four agencies are down to the final pitch for the PR brief, which covers just under 500 supermarkets across the UK.
Morrisons kicked off a review of its consumer PR account last month, deciding to split it in two. A separate pitch for a brand PR brief will take place in the next two months.
3 Monkeys had held the combined consumer PR account for the past four years.
Morrisons' financial PR account, which is handled by Citigate Dewe Rogerson, is not being reviewed.
The supermarket group declined to comment.