The Uruguay international, who received a seven-match ban for a similar incident while playing in Holland, appeared to sink his teeth into the Chelsea centre-back
With the Anfield outfit trailing to the Blues, and having given away a penalty moments earlier, Suarez seemed to grab Ivanovic's arm and sink his teeth into the defender after a coming together between the pair.
The Serbian international gesticulated that Suarez had bitten him, appealing to the referee, but the incident was not spotted by the match officials.
Suarez, no stranger to controversy, was involved in a similar affray while at Ajax, where he was handed a seven-match ban for biting PSV Eindhoven midfielder Otman Bakkal.
On that occasion, the referee did not spot the incident at the time - despite Bakkal lifting his shirt to reveal bite marks - but the Uruguayan was retrospectively handed a lengthy ban and fined by his club.
It is not the first time a Premier League player has bitten an opponent, with Jermain Defoe having nibbled on West Ham midfielder Javier Mascherano in October 2006.
The Tottenham forward bit the Argentine on the shoulder, but was booked by referee Steve Bennett preventing the FA from taking retrospective action.