The fashion retailer said in a statement that it had received an indicative approach for the business, which was not materially above the closing mid-market price of 211.5p on February 2.
The independent directors said that the approach was at a very preliminary stage and that any proposal was likely to be subject to a number of material pre-conditions. The company stressed that there was no certainty that any offer would result.
Analyst Seymour Pierce speculated that the approach could be from property investor Dawnay Day, which is known to be acquisitive. The investment group bought Austin Reed and Country Casuals last year.
Alexon sold its struggling shoe chain Dolcis for about£3 million in December.