The incident occurred late on in Liverpool's 4-1 Premier League win at Anfield as the players chased a ball.
As Ivanovic attempted to shepherd the ball out for a goal kick, Suarez appeared to haul the Serbian down.
Referee Kevin Friend did not award a free-kick, and if it is established he did not see the incident, Suarez could face retrospective action.
The Uruguayan was banned for eight matches earlier this season when he was found to have racially abused Manchester United's Patrice Evra,
Ivanovic could count himself lucky still to be on the pitch at that stage - earlier on he conceded his penalty by delivering a forearm to the midriff of Liverpool striker Andy Carroll.
Referee Friend settled for a yellow card, meaning Ivanovic cannot face any further action.