While not denying the claim, the BBC said the figures were "inaccurate".
The report, in this week's The Radio magazine claimed the station lost 372,000 weekly listeners in February and more in March.It said the audience figures could plunge to their lowest since the station began in 1967.
The alleged decline accelerated after the exit of Chris Evans, the magazine said. But it could also be due to the growth in popularity of Radio 5 Live and Steve Wright's hugely popular Saturday morning show on Radio 2.
Wright's audience increased by 150,000, according to the last published independent figures.
The last officially audited Rajar ratings showed Radio One attracted more than 10.6 million weekly listeners. It would have an estimated weekly audience reach of about 10.14 million if the new figures are correct.Reuse content