The brand currently spends less than £2m on advertising. The incumbent agency is WARL Change Behaviour with media handled by The Media Shop.
The review puts a question mark over the future of Jazz FM's long-standing rainbow-coloured chameleon mascot.
GMG, which acquired the station for £44.5m six months ago, has applied for new radio licences in the West Midlands and Glasgow, expanding beyond its current base in London and the North West.
As well as the core radio station Jazz FM 102.2, the company operates a small number of record labels including Jazz FM - selling compilation CDs at premium prices - Onion, and Hed Kandi, aimed at a younger, funkier generation of jazz music followers. However, the company is understood to be only reviewing the radio station's advertising.
Jazz FM's head of marketing Nicola Thompson refused to comment on the review.
Jazzfm.com's 800,000 unique visitors,make it the world's largest web radio broadcaster according to audience measuring service Measurecast.