The BBC reports the search relates to allegations the Methodist minister bought and used illegal drugs, including cocaine.
Flowers, 63, apologised after he was filmed allegedly buying drugs, the report said.
Yesterday, the current chairman Len Wardle quit his post over the scandal.
Business secretary Vince Cable told the BBC there had been “a serious failure of regulation”.
The Telegraph reports former City minister Paul Myners has said the bank’s £1.5bn recapitalisation deal could be under threat in the wake of the scandal.
A spokesman for West Yorkshire Police said: “Officers executed a search warrant at an address in Hollingwood Lane, Great Horton, Bradford, yesterday [Tuesday] as part of their investigation into alleged drugs offences arising from a national Sunday newspaper story.”
The Mail on Sunday filmed Flowers apparently buying illegal drugs. The sting took place days after Flowers – who headed the lender from April 2010 until June this year – appeared before the Treasury Select Committee.
