The alleged incident occurred as the players tussled after on-loan Liverpool defender Beck was sent off for kicking out at an opponent in the 89th minute of the goalless draw.
Osmajic received a yellow card following the incident.
"He's got a big bite mark on the back of his neck," Blackburn head coach John Eustace said.
"It's a very serious incident, nobody likes to be bitten. Everyone is angry about it. It's not a nice situation to be in. I'm sure the right people will see it and deal with it."
The FA said in an emailed statement: "We're aware of this incident and will be looking into it."
Preston manager Paul Heckingbottom said he had not seen the incident.
"All I can say is that there is no place for that and we know we can’t do that," Heckingbottom added.
"Mistimed tackles, things like that are part and parcel of the game, you accept them. Anything that is not, we know how that’s dealt with."
In 2013 the FA banned Luis Suarez for 10 matches after the Liverpool forward bit Chelsea defender Branislav Ivanovic.
