Mustoes, Cogent Elliott and Golley Slater will pitch for the business, which includes a heavyweight TV strategy.
The pitch is being handled by Agency Insight, and a decision is expected by next month.
The review comes as Screwfix looks to push its services to the trade sector and amateur home improvers.
Simon O'Mahony, the head of marketing at Screwfix, said: "Each agency has been asked to develop an approach that reflects the current status of the business."
He added: "We are currently reviewing storyboards and will be announcing our decision shortly."
The company's last retained agency was WWAV Rapp Collins, which worked on the business until 2005.
Screwfix is the UK's largest direct and online supplier of trade tools, accessories and hardware products. It is owned by Kingfisher, an international holding company that also owns B&Q, Castorama France and Koctas.