City sources said that the 126-year-old business could fetch £100m after its transformation into a label with 46 UK shops, including four in Yorkshire.
Mr Tillman bought the firm for a token amount in 2003 when its annual losses stood at £12m. Last year it achieved earnings of £7m on sales of £86m and said it planned to increase its international footprint.
The entrepreneur, who is chairman of the British Fashion Council, appointed Belinda Earl, the former chief executive of Debenhams, soon after taking over the firm and they have since helped revive its fortunes.
As well as branching out into new areas, such as accessories and fragrance, they have also launched the brand online to broaden its customer base. In 2009, Mr Tillman bought luxury label Aquascutum.
According to a Sunday newspaper report, he has appointed investment bank Rothschild to consider the firm’s strategic options, including an outright sale.