Coventry Building Society, the third biggest in the UK, is in the early stages of merger talks with smaller rival Stroud & Swindon.
This could create a combined group with more than £20 billion in assets.
However, Coventry said the merger "would only proceed if it were to the benefit of both sets of members".
Linda Will, Stroud marketing director, said the board was considering the proposal but added that no final decision had been made.
"There are no offers on the table. It is part of the board's fiduciary duties to consider an approach from any credible partners."
Demands by the Financial Services Authority (FSA) that building societies hold more capital has led to increasing pressure for them to merge. But Will denied this was the case.
"We are not being forced by the FSA," she said. "We hold a huge amount of capital."
Stroud has 265,000 members and holds just under £3 billion in assets. Meanwhile, Coventry has 1.2 million members and a 48-strong branch network across the Midlands.
The decision by the Bank of England to keep interest rates low contributed to Stroud recording a loss of £3.4 million in 2008. Meanwhile last week, Coventry reported pre-tax profits had more than doubled in 2009 to £56.2 million.
The move follows the tie-up between Skipton Building Society and its loss-making rival Chesham, which was announced back in February as another wave of consolidation ripples through the sector.
The enlarged group, which will be called Skipton Building Society, will have a 92-strong branch network and £15 billion worth of assets.
Last year, Britain's second largest mutual Yorkshire Building Society merged with loss-making rival Chelsea. Meanwhile, Nationwide - by far Britain's biggest building society - has stepped in with takeovers of the Cheshire and Derbyshire building societies.