A tie-up would form a business with more than six million customers and £70bn of assets, although both sides stressed that talks were at an early stage.
A legal change due to come into force by the end of this year or early next will make it possible for different types of mutuals - building societies, co-operatives and friendly societies - to join forces. At present, there is no legislation in place to allow this to happen.
Both organisations are in sound financial health and believe a tie-up could offer a customer-owned alternative to the plc market.
As well as speaking to the Britannia, CFS - led by chief executive David Anderson - said it had been in contact with other parties about how its products can be sold in their branch networks.
The Co-op said: "We have ambitious growth plans and have had discussions with a number of parties including Britannia about how we can work more closely together for mutual benefit.
"There are clearly a range of possibilities open to us but we will only take action which benefits further the clear momentum occurring now within the co-operative and mutual sector."
The Co-op has weathered the turmoil in money markets because it is fully funded by customer deposits. Last month, it announced a 90 per cent rise in underlying half-year profits to £73.4m and said its bad debt levels had fallen.
It has also been boosted by £20m worth of deposits as savers spread their money between institutions amid fears over the security of Britain's banks.
Britannia, which is based in Leek, Staffordshire, has a 245-strong branch network and 2.6 million savers. It has 365,000 members in the north west.
It is not clear whether Britannia's three million members would receive a windfall payment as part of any merger with the Co-op.
Britannia boss Neville Richardson said it was too early to comment about the impact on customers and staff.
Tweet

Showing comments 1 to 2 and replies | View All
brian frankling (16/10/2008 at 18:17)
What of that other giant of the mutual world Nationwide.
it is reported that this mutual building society has gone for financial help to the Bank of England, why is this, is it mutual in fact or just in name, esp. as it is a busy bee gobbling up the Portman and now others in the pipeline....is this a building society...or a Bank pretending to be a building society. can you help me understand this enigma?
naz, Manchester (18/10/2008 at 19:54)
The mutual sector is not immune from the financial crisis with mortgage lending grinding to a halt.