Gerrard struck Brown with a forearm to the back of the Portsmouth ace’s neck in the second half of Liverpool’s 4-1 win.
Gerrard could be charged for violent conduct and get a three-game suspension.
An FA spokesman told The Mirror: “We need to establish what the referee gave the free-kick for. Whether it was for an element of what he saw or whether it was for the entirety of what we have all seen since on TV.
“We will be working on this basis and gathering the referee’s report.”