The former couple, whose turbulent on-off relationship was well documented in the press, split up last summer.
The singers would follow the latest celebrity pairing by the clothing brand, which brought together Madonna and hip-hop star Missy Elliot in a set of TV ads. The pop divas are promoting Gap corduroys with a version of Madonna's 80s hit 'Into the Groove'.
Celebrities have formed a major part of Gap's advertising in the past few years and helped the brand stem declining sales. In its latest trading statement, Gap said sales for the five weeks to July 5 were $1.5bn (£930m), up 13% on the same period last year, when sales were $1.3bn.
Other celebrities the retailer has used include Marianne Faithfull and Willie Nelson, Ryan Adams, Dennis Hopper, Kate Beckinsale and 'Lord of the Rings' star Orlando Bloom.
Last year, Gap hired Laird & Partners to handle creative advertising after a period of handling the work in-house. In December, it appointed Leo Burnett to work on refining brand positioning and developing longer-term marketing strategies.
This followed the appointment of Optimedia to handle its £30m pan-European media account after it moved it out of Mediaedge:CIA.
Timberlake is also thought to be in talks about a $1m deal to provide vocals for a new McDonald's jingle and to take over from Ronald McDonald as the face of the burger chain in its 'I'm Lovin' It' campaign.
Timberlake worked with McDonald's for a 2000 compact disc promotion while with the pop band N'Sync for McDonald's World Children's Day.
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