Unite said its members voted against a 2.5 per cent offer, arguing it was lower than the RPI rate of inflation so represented a real-terms pay cut.
If members vote for strike action then the supermarket giant could see empty shelves this winter which could potentially affect the Christmas period.
Supermarket shelves have been empty in recent weeks as a result of a shortage in lorry drivers
The distribution centres involved are in Belfast, Didcot, Doncaster and Thurrock
Unite general secretary Sharon Graham said: 'Tesco's staff have kept working throughout the pandemic and that alone surely means they deserve a decent pay rise. Instead, they are being offered