Mr Dunn added: “Our listing on Aim for the past 20 years has been an important part of Asos’s development, but the time is now right to move to the main market.”
Nick Beighton, the former chief executive who left abruptly in October amid a profit warning, had previously shown little enthusiasm for such a shake-up.
In a trading update, Mr Dunn also said sales remained below pre-pandemic levels but were higher than last year when Covid restrictions were in force.
Revenues rose by just 2pc to £1.4bn in the fourth months to December 31 and profits took a hit as Asos was forced to spend more on wages, shipping and discounting.
It has increased wages for warehouse staff again and was forced to air freight more stock as global supply chain bottlenecks continued to affect shipping routes.
Rising costs also meant Asos had to increase prices by the “low to mid-single digits”.
Sales of dresses and other evening wear improved compared with 2020 but returns jumped over the Christmas period as parties were cancelled.
Mr Dunn said sales had still not recovered to pre-pandemic levels but he felt more confident about 2022, despite the threat of inflation and rising energy bills to consumer spending.
He claimed shoppers had saved money during the pandemic and would prioritise clothing over other purchases as due to many having not bought many new outfits during the period of restrictions.
Trading was “nowhere near back to where it was pre-pandemic”, Mr Dunn said.
Underlying annual profits were expected to rise by between 10pc and 15pc to between £110m and £140m.