The Uruguayan striker - who later went on to score a 97th-minute equaliser - tangled with Ivanovic during the second half of the Sky Live Premier League clash at Anfield, which finished 2-2.
Referee Kevin Friend did not see the incident but television pictures are conclusive and the FA is almost certain to act, with Suarez likely to be handed a lengthy ban.
Suarez, who has apologised to Ivanovic, has previous in relation to biting as, immediately prior to joining Liverpool in January 2011, he served a seven-match ban while at Ajax after sinking his teeth into PSV Eindhoven midfielder Otman Bakkal.
That will have no bearing on what action the FA takes, however, as it was under a different association.
It has been reported that Ivanovic was also spoken to by Surrey Police at the club's Cobham training ground after complaints made to Merseyside Police were passed on to their southern colleagues, who wanted to ascertain whether the defender had sustained any injury.
That was found not to be the case and Ivanovic told police he did not want to press charges.