Civilian workers employed by British Transport Police are ready to walk out next weekend, when thousands of fans will be travelling to Wembley.
Their union, the Transport and Salaried Staffs' Association, said this could create problems for train operators involved in ferrying fans to both the Arsenal v Chelsea game on Saturday April 18 and Manchester United v Everton the following day.
If there is no settlement, the TSSA plans a further walkout on the weekend of the Cup final itself.
The workers involved are responsible for deploying officers to areas when and where they are needed.
If fans behave, the impact on the matches would be limited. But if there is any trouble and transport police are not sent quickly, train and tube drivers could stop the trains and remove themselves to a "place of safety".
British Transport Police sought to play down the impact of the threatened strike.
"It is unfortunate that TSSA has decided to take this action," said Alan Pacey, the force's assistant director of operations.
"The force has already put in place robust arrangements to ensure our control rooms continue to respond to emergency and non-emergency calls for assistance and continue to effectively deploy our resources across the network.
"We are not anticipating any travel disruption as a result of the proposed industrial action over the semi-finals weekend. Passengers, football fans and rail staff should be reassured that BTP will continue to police the network and respond to incident."