Chelsea and the Metropolitan Police are investigating an incident at Stamford Bridge in which a fan confronted Newcastle goalkeeper Martin Dubravka.
The fan appeared to push Dubravka on the pitch in the aftermath of Chelsea's injury-time equaliser on Tuesday.
Stewards ushered the fan away but lengthy discussions between referee Jarred Gillett and Chelsea security staff followed before the penalty shootout.
No arrests have been made as yet.
Chelsea won the EFL quarter-final tie on penalties after the game had finished 1-1, with Kieran Trippier and Matt Ritchie unable to convert for Newcastle.
Speaking after the game, Chelsea manager Mauricio Pochettino said: "We need to be careful.