Mr Forth, an arch-Eurosceptic MP, had a majority of 13,342 over Labour at the last election.
There are private Tory fears that, given Mr Forth's stridently anti-European Union views, the UK Independence Party may be the most dangerous challenger.
Nigel Farage, Ukip's leader in the European Parliament, said last night that he himself was "seriously thinking" of standing in what was a "must-do" by-election for his party.
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