The Leeds company develops, manufactures and supplies liquid medicines for patients who have difficulty in swallowing tablets and capsules.
It is highly profitable and last year made a pre-tax profit of £14.63m on turnover of £35.81m.
Private equity firm CBPE bought the business for just under £100m in 2006 and has asked corporate financers at Rothschild to find a new owner.
It is thought that the sale could raise £200m for CBPE and the Rosemont management team, which would make it one of the biggest Yorkshire deals seen in recent months.
The Yorkshire Post understands that an agreement could be in place to sell the business early next year.
A spokesman for London-based CBPE declined to comment.
Rosemont invests heavily in research and development – £3.33m last year – to expand its product portfolio to keep it ahead of generic competition in the UK pharmaceuticals market.
The company developed 17 new products last year for customers including hospitals, wholesalers and retail pharmacies.
Its range of oral medicines is designed to improve the lives of patients with swallowing difficulties, which typically affects young children and the elderly.
Rosemont’s main market is the UK, but the firm is pursuing opportunities overseas in the US and Europe.
The company triumphed in the £10m to £50m category in last year’s Yorkshire Post Excellence in Business Awards.