According to Sky News, Interritus Limited and Al Faisal Holding have "held several rounds of talks" with Co-op Bank, however sources say there are "a series of significant hurdles to any deal being agreed".
Interritus and Al Faisal are reportedly attracted to Co-Op's 'ethical credentials'.
Last month Virgin Money abandoned takeover talks, and Co-Op was then thought to be seeking a deal with its US hedge fund investors.
In a statement in February, the Co-Operative Board said the sale was "something always considered a potential outcome of the turnaround plan" and announced that it was inviting offers for all of the issued ordinary share capital of the Bank.
It is also considering ways to raise equity capital from existing and new capital providers and a potential liability management exercise of its outstanding public debt.
The Bank hopes to raise around £700m in capital and between £250m and £300m from issuing new shares.