The company was bought by New York-based Apollo Global Management in 2012 and it is believed that Apollo are leading the public listing plans which are still at an early stage.
The news comes six months after Apollo abandoned similar talks with its investors. It is thought that the new plans could prompt expressions of interest in the company that retail analysts estimate could be worth around £600m.
The company also recently expanded into the US market with the $100m (£75.5m) acquisition of Mayors Jewellers. Aurum currently boasts just under half of all Rolex sales and has a 36.4% share of the watch market in the UK.
It has around 150 physical stores in the UK and over 1700 employees.
Retail Sector has reached out to Aurum Holdings for comment.