A final decision has not yet been taken, but it is understood Labour leaders favour either Thursday, 30 October or Thursday, 6 November for the contest.
The November date is the favourite simply because it comes only a day after the expected result of the American presidential election, and if Labour was to lose, party managers believe the bad news would be partly buried by the US coverage.
Gordon Brown was in Fife yesterday on constituency business, and although senior Labour sources stressed that no decision on the timing had been made yet, it is understood that the Prime Minister favours a long run-in to the crucial poll.
Labour will choose its candidate next Monday. One early front-runner is Lindsay Roy, the headteacher of Kirkcaldy High School.
The by-election was caused by the death of John MacDougall, the Labour MP, from lung cancer.
The SNP is favourite to take the seat, which Labour holds with a 10,600 majority.