The mutual has begun exploring options such as issuing a form of capital known as permanent interest-bearing shares (PIBS) which would be sold to new investors to fund the deal, according to Sky News.
Bid plans, which would probably involve the Coventry raising between £300m and £400m, have reportedly been worked on for several months.
The Coventry has held talks with the Financial Services Authority (FSA) about ensuring the new funding qualifies as core tier one capital for regulatory purposes.
People close to the situation have said the building society might seek to create a variant of PIBS in order to fund a deal.
News of discussions about capital-raising options come as ministers prepare to offload Northern Rock.
UK Financial Investments (UKFI) will hold a board meeting later this week to finalise preparations for a sale of the bank, according to Sky.
