Gascoigne is alleged to have elbowed Spurs midfielder Oyvind Leonardsen.
"The video will be studied before we consider whether any action is to be taken," said a spokesman for the FA, who will also review Mark Viduka's tussle-with Martin Keown during Sunday's draw between Leeds and Arsenal.
Everton can ill afford any further losses to their already depleted midfield but Leonhardsen was adamant Gascoigne should have been punished by referee Clive Wilkes.
The Norwegian exclaimed: "If the referee had seen them Gazza would have been sent off. He should have been sent off too as they were both red card offences. It was very painful and out of order.
"I admit I caught him early on with a tackle but for the rest of the game we had a battle. He went for me. A player of his quality and reputation shouldn't be doing those things.
"I think he lost his head in the first half but when he calmed down he said sorry and we shook on it at the end."