The Public and Commercial Services (PCS) union – which represents 15,000 Border Force, passport, and visa staff – is expected to announce its December strike dates on Wednesday (7 December).
The government has reportedly put 600 military personnel and a number of civil servants on standby to be deployed to airports to help alleviate pressures.
But according to industry bosses, the reinforcements "will not be enough" to avoid a number of flight cancellations over the festive period.
An airport chief told The Telegraph: "Border Force haven’t given us any indication of what resources might be available or how many of their staff might be called out on strike.
"There is going to be some impact and there is concern we cannot keep people just flying into the country and waiting in halls in long queues. We will have to make cancellations because there is no way of getting people through the border."
