The US fitness company is run through franchises in more than 200 locations around the UK.
It offers a fitness programme designed for women, aimed at fast and sustainable weight loss through 30-minute cardio and strength workouts. There is also an accompanying diet programme.
The pitches will take place in early July. Four agencies are believed to be on the pitch list, with the winning shop tasked with creating a through-the-line campaign that could include TV work.
The campaign is thought to be aimed at relaunching Curves in the UK and boosting its profile to grow business.
Curves was launched in Texas in 1992 by Gary and Diane Heavin, and claims to have around 8,000 clubs in more than 90 countries, serving more than four million women.
Curves did not respond to requests for comment.