Private equity firm Hanson has reportedly held initial talks with Credit Suisse First Boston about a potential RHM flotation.
The food group is thought to be worth around £1.5 billion and has sales of around £1.7 billion thanks to strong brands including Mr Kipling cakes and Hovis bread. Hanson tried to float RHM in 2002 but abandoned the plan.
A new move for the stock market later this year would appear to fit with RHM's current push to reorganise its ailing pension fund, which sits around £525 million in debt, and recent actions to restructure its business.
The firm said it wanted to complete its pension reform by September this year and measures included: new pension contribution rates, new definitions of pensionable earnings, lower national insurance costs, limits to discretionary pension increases paid in retirement and limits on early retirement terms.
RHM is also in advanced negotiations with two US companies - Keystone Foods and East Balt Guenther Bakeries - to sell its Golden West bakery, ending a troublesome supplier relationship with fast-food giant McDonald's and streamlining the company's focus on its big brands.
Accordingly, the firm recently reorganised its four business units into three.
The three divisions - Cakes and Customer Partnerships, Culinary Brands and Bread Bakeries - "will help us to continue to build on our focus on profitable business performance, while unlocking further opportunities for brands, customers and product synergies", according to RHM chief executive Ian McMahon.
Any stock market flotation later this year would also probably be based upon the value of RHM's flagship brands, and the company said in February it would spend £8 million re-launching Mr Kipling cakes as a premium product.
Similar treatment is expected for Hovis in the near future, not least to try and maintain the brand's value in the face of falling white bread consumption in Britain.
In 2004, Britons ate two fewer loaves each than in 2003, per capita consumption dropping from 46.8kg to 45.3kg, according to the latest Datamonitor research.