The party's general secretary Iain McNicol is understood to want to move a £1.2 million loan to the trade union-controlled Unity Trust Bank.Its current account facilities are also expected to be shifted.
The move comes after a tumultuous period for the bank, which has seen big losses and the resignation of chairman Paul Flowers, who is now facing drug possession charges.
It would effectively draw a line under a financial relationship going back nearly a century.
The Co-operative Movement and Labour joined as parties in the 1920s and the link-up with the banking arm is believed to have started then.
Labour stressed that the change of tack was for "commercial reasons", but the controversy over the past year is thought to have strained relations.
The BBC reported that the bank - which is now 70% owned by American investors - was also keen to become "apolitical".
Labour are attempting to cut their debt burden, with £25m owed in 2006, and £4.5m owed now.
The Co-op has announced losses of £2.5bn, with £2.1m of the figure down the the organisation's banking arm.
A report into the bank's near collapse is expected to blame poor governance and the takeover of the Britannia Building Society for many of its current problems.
A party spokesman said: "All decisions are taken for commercial reasons."