Rooney was targeted during Manchester United's match at Crystal Palace and drew the referee's attention to missiles being thrown at him.
The FA had a crowd control adviser at the game and is waiting for a report into the incidents. It is also contacting Crystal Place to ask for their observations and speaking to the police in charge of security inside the ground.
Palace are unlikely to be charged unless the investigation decides the club was negligent - the main aim of the probe is to see if any of the people who threw coins or other items at the England striker can be identified from CCTV footage.
Any fan throwing coins faces a potentially lengthy banning order from magistrates.
United defender Rio Ferdinand suffered a cut above the eye after being struck by a coin during a derby match at Manchester City in December 2012.
Police are still looking into Theo Walcott being targeted by missiles during the Arsenal's FA Cup third round victory against Tottenham last month.
Crystal Palace co-chairman Steve Browett has vowed to ban anyone found to be responsible from the club.
Speaking about a pre-match display organised by fans, he said on the Crystal Palace 'Five Year Plan' podcast: "I was really angry because you've got guys who worked through the night on Friday night, they have worked really hard on that display.
"They've spent hundreds, thousands of hours getting that display right and you turn on Match of the Day and they don't even mention it, all you see is some t**t throwing a coin at Wayne Rooney.
"One idiot has screwed it up for everybody else and it makes me so angry. I hope somebody turns him in because he's not welcome at Selhurst Park."