The sale was put on hold earlier in the year due to heightened market uncertainty after the Brexit vote.
The Treasury has now given the go ahead for UK Asset Resolution (UKAR) to begin sale proceedings once again, according to a report by The Times.
Non-disclosure agreements are scheduled to be sent out to potential buyers this week.
Bradford & Bingley was bailed out by the government in the 2008 financial crisis after heavy buy-to-let lending and debt led to a collapse in its shares.
UKAR was set up to manage both Bradford & Bingley and Northern Rock in the wake of the 2008 crash.
Some £13bn of residential mortgages previously issued by Northern Rock were sold to Cerberus, an American private equity firm, and £3.3bn were sold to TSB Bank.