The Rail, Maritime and Transport Workers Union (RMT) believes taking staff data in this way can put them at risk, and has labelled the method "draconian" in making employees seem like criminals.
The cleaners' employer, Carlisle Cleaning Services, is currently in talks with the RMT to come up with a solution.
But RMT general secretary Bob Crow said: "The introduction of routine staff finger printing is totally outrageous and further proof that our surveillance society is spiralling out of control. Carlisle Group cannot be allowed to introduce these Orwellian working practices."
The ballot for industrial action will open on 21 April 2009 and close on Tuesday 5 May 2009.
St Pancras Station cleaners may strike over 'draconian' digital 'clocking in' methods
More than 100 cleaners at St Pancras Station in London are considering strike action over plans to introduce machines for them to clock in and clock out using their fingerprints.