Chappell is understood to have been arrested at his home near Blandford Forum, Dorset, early on the morning of November 2, according to the Sunday Times.
HMRC confirmed that it had arrested a “49-year-old businessman”, the paper said.
The UK tax office is also believed to have raided an office near by belonging to Chappell.
Chappell bought two yachts, a Bentley and several Range Rovers during his time at BHS.
The closure of all of BHS’s stores after it went into administration left a £571m ($748m, €681m) pension deficit.
Earlier this month, the UK’s Pensions Regulator (TPR) launched enforcement actions against Chappell, and previous BHS owner Philip Green, aimed at seeking redress for 20,000 pension scheme members.