Two of the Silverstone based team's staff members returned to the UK earlier this week after a Molotov cocktail incident.
The BBC is reporting rumors that other members are the team are now refusing to travel from the circuit back to their hotels after dark.
That would mean Paul di Resta and Nico Hulkenberg will not be able to practice in the second 90 minute session scheduled for 2pm local.
The BBC said the rumor ties in with Force India's drivers unusually running soft tires in the initial practice session on Friday.
And F1 chief executive Bernie Ecclestone called the team's deputy principal Bob Fernley off the pitwall during the initial practice session for talks.
Force India said it "wouldn't want to comment".