He was allegedly arrested for failing to pay more than £500,000 tax on money from the department store, according to the Sunday Times.
An HMRC spokesperson said: "We do not comment on identifiable cases, but can confirm we have arrested a 49-year-old businessman."
The arrest took place on 2 November.
The watchdog is hoping to secure a £350m payment from Green after the collapse of BHS in April left a £571m deficit in the company's pension scheme, which has 20,000 members.
Green, the parent company of his empire Taveta Investments, Chappell, and his company Retail Acquisitions were each been sent warning notices – setting out evidence to support the use of contribution notices and financial support directions, which would demand money from the parties.
BHS’s pension deficit stood at £571m when Green sold the company to Chappell’s Retail Acquisitions for £1 in March last year.
Lesley Titcomb, head of the pensions watchdog, said: “Our decision to launch enforcement action is an important milestone in our work to attain redress for the thousands of members of BHS schemes who have been placed in this position through no fault of their own.”
Chappell bought BHS through Retail Acquisitions, a consortium of which he owned 90 per cent. It collected an estimated £17m from BHS despite owning it for just 13 months before it collapsed. Green was in charge of the retailer between 2000 and 2015, during which time his family and other shareholders collected over £580m.