It is understood that NBNK will merge with NAB-owned Clydesdale Bank and Yorkshire Bank to table a combined offer for the Lloyds branches as well as Northern Rock.
If the bid is successful it would create overnight one of the largest banks in the UK with more than 900 branches and deposits in excess of £40bn.
Virgin Money has tabled a rival bid for Northern Rock and has already gained backing from major investors including US billionaire Wilbur Ross, private equity firm Carlyle Group and the Universities Superannuation Scheme.
The combined NBNK-NAB would be a primary competitor to Virgin Money and a Telegraph source with knowledge of the talks said the deal would offer NAB a way to exit the UK as the business would be listed on the London market enabling it to sell down its stake over time.
NAB and Lloyds Banking Group declined to comment. NBNK was not immediately available to comment.
Rob Clifford, former managing director at Virgin Money and director at If I Were You, said: “It would not be a surprise if a merged entity created the access to capital and breadth of management expertise required to take on the Lloyds disposals, as such a deal could give smaller firms serious indigestion.
“This looks more like a plan which enables an elegant exit from the UK for NAB to me, than a deal borne purely out of a strategy to absorb the Lloyds branches.
“The reported merger seems to make sense but I doubt it could deliver anywhere near the executive focus and consumer appeal that Virgin Money has.
“I can't see such a move giving Virgin anything to lose sleep about, given their reputational prowess.”