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In a statement, the building societies said: "The proposal follows swift, pre-emptive action from the board of the Barnsley in approaching the Yorkshire to seek a merger after the identification of possible losses of deposits with Icelandic banks."
Barnsley currently holds assets of £376 million and has said its exposure to Heritable and Kaupthing Singer & Freidlander could lead to the loss of £10 million, reports Reuters.
Last month, the UK's largest building society Nationwide announced it is to merge with the Cheshire and the Derbyshire building societies.
Meanwhile, the Britannia Building Society is in exploratory merger talks with the ethical Co-operative Bank.
According to the Press Association, officials from the government and the Bank of England are to travel to Iceland in search of compensation for savers in the UK.
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