It told shareholders that Mr Dunkerton “is engaged in discussions with potential financing partners” over a possible takeover offer for the business.
Mr Dunkerton, who co-founded the brand in 2003, already owns roughly 26% of the business.
The retail firm said “discussions are at a preliminary stage and no decisions have been made”.
The business, which employs around 3,350 globally, runs 216 shops alongside franchised stores.
Earlier this week, Superdry said it was working with advisers to look at various “cost-saving options” for the business.
It came after Sky News reported it could launch a restructuring plan or Company Voluntary Arrangement (CVA).
Such a move could result in store closures and potentially force through rent reductions with landlords.
Last week, Superdry said that its revenue had fallen by nearly a quarter (23.5%) to £219.8 million in the six months to the end of October, with adjusted loss nearly doubling to £25.3 million.