He said the firm, which has 18 stores in cities across the US, wants to have physical retail space in Britain before the end of the year.
Eis, who heads the firm’s international business, said: “We’re looking for an offline partner in the UK. What we are after is to have either showrooms or a retail partner.
“What people want is a frictionless shopping journey. They want to be able to start the process online and finish offline and vice versa.”
Casper entered the UK market in 2016 and earlier this year its British business moved into profitability, having enjoyed annual triple-digit growth since launch.
The firm and its fellow bed-in-a-box online mattress firms have grown quickly at the expense of traditional retailers.
Casper and its online rivals account for five per cent of the market and Eis believes that they could have 30 per cent within the next five years.
Casper, whose investors include Leonardo DiCaprio, Ashton Kutcher, Tobey Maguire and 50 Cent, offers a 100-day trial of its mattresses, as well as disposal service.