Joe Hart has said he was hit by a toilet roll and that other objects including a lighter, marker pen and bottle of water were thrown at England players by Montenegro fans during Tuesday's draw in Podgorica.
Fifa is waiting for official reports before deciding if Montenegro has a case to answer.
The Football Association will be sent documentation from its own personnel at the match before deciding if it wishes to make a complaint.
Wayne Rooney, Steven Gerrard were also targeted, alongside Joe Hart, who said of being hit by a toilet roll: "It pinged off my head and wrapped round my shoulder – but it's not going to kill you, is it? It's not ideal, but that's the beauty of football."
Regarding what else was flung at the players, Hart said: "You get all sorts of things thrown at you. It was a lighter. There was a marker pen. All sorts. Anything they have to hand. A big bottle of Evian."
A statement from Fifa said: "We are still collecting all the post-match reports, since the officials have got twenty-four 24 hours to send them. Based on the mentioned reports, Fifa will proceed accordingly."
After the game in which Rooney's early goal was cancelled out by Dejan Damjanovic's second-half strike, there were claims that the stadium announcer swore at the England team and aimed abuse at them. But according to Ivan Radovic, a Montenegro FA spokesperson, it was from a fan with a megaphone and not the official announcer.
Radovic said: "One hundred per cent it was not him. I was stood next to him all game and I know he did not say anything like this. He is part of the official Montenegro [organisation] so he would not say anything like this."