Tillman signalled he was mulling his own offer for the UK fashion retailer, according to reports.
Tillman has admitted to having recent talks with both the board and major shareholder Guy Naggar over a possible bid.
On Friday, Austin Reed declined a 131 pence per share bid approach from Naggar and Peter Klimt, who together own just under 30 per cent of the shares. The retailer said the offer undervalued the group.
An Austin Reed statement said: 'The Board has reviewed this approach carefully, in conjunction with its financial advisers, Close Brothers and believes that the level of the proposed cash offer significantly undervalues Austin Reed and its prospects. The Board has unanimously rejected the Minority Shareholders' approach and urges shareholders to take no action at this time.'