Yorkshire Building Society - which has around 2.8 million members and assets worth more than Â£30 billion - claimed the proposition could result in the market becoming even tougher for mutuals, the Yorkshire Post reports.
Andy Caton, corporate development director at Yorkshire, stated such a move would imply more concentration in the market.
The industry figure explained: "Just by combining the two, that might reduce the pool of possible people interested in it. It could be self-defeating."
A larger field that includes smaller, better-managed players instead of a focus on those that are considered too big to fail could be the best way forward, Mr Caton observed.
The comments come as both Yorkshire Building Society and Coventry Building Society consider making bids for Northern Rock.
By Asim Shah