Sources close to the investor told The Times newspaper, a shareholder was considering whether to mount an counter offer. He is understood to have sounded out potential allies in a possible consortium and is in talks to secure funding.
Members of the Moss and Gee families, which control a combined 27% of the shares in the company are understood to have been approached by the investor.
The Times quotes a source as saying: "There is a clear feeling that for the past 18 months the management at Moss Bros have been besotted with Baugur that they have taken their eye of the ball with regard to running the business. People in the market are valuing the management, not the assets, which we feel are worth more than Baugur is willing to pay.
On Monday Baugur tabled an indicative offer of 42p per share, valuing the business at around £40 million.