Burkitt DDB lost the retailer's £13m creative account to Lowe last month.
The shortlist for the media account consists of Interpublic Group agency Universal McCann, Omnicom's Manning Gottlieb OMD and independent media shop BLM.
Naked may clinch a communications planning brief for the retailer after it was asked to present work.
The John Lewis marketing director, Andrew Woodward, and commercial director, Brendan Sweeney, are overseeing the pitch, which is being handled by media auditors Billetts.
Shortlisted agency Manning Gottlieb is thought to be in pole position as it already works on John Lewis Group's £9m Waitrose media account.
The agency won the Waitrose business as part of a five-way pitch involving Havas-owned Media Planning Group, WPP's MindShare, Aegis-owned Vizeum and Interpublic's Universal McCann. Sister agency OMD also handles the bulk of media buying for the John Lewis business.
John Lewis is a heavy press advertiser, spending £9.9m on the sector according to Nielsen Media Research.
It also spends £2.1m on television and an estimated £2.3m on direct mail campaigns to complement its press spend.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .