Linda Will, sales and marketing director at Stroud & Swindon, said the building society is in very early stage talks about which there is no detail.

A statement from Coventry also confirmed talks are happening, but stressed that no decision has yet been made.

It said: “There is no certainty that these will lead to a merger, which would only proceed if it were to the benefit of both sets of members.”

Coventry, the third largest building society in the UK, has assets of £18.4bn. It recently posted 2009 pre-tax profits of £56.2m. It lent £0.9bn in mortgages in 2009.

Stroud & Swindon has assets of more than £2.5bn.

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Any merger would require approval from the members of both societies and from the FSA.