The Uruguay striker has since apologized to Ivanovic for his "inexcusable behavior" during Sunday's 2-2 draw at Anfield, and he has also been fined by the club, but he will likely face a lengthy ban from the Football Association.
The 26-year-old was suspended for seven matches during his time with Ajax for biting PSV's Otman Bakkal, and he sat out eight Premier League matches last season for racially abusing Patrice Evra.
Gordon Taylor, the chief executive of the PFA, says his organist will offer help to the controversial forward.
"There is no doubting his football ability, that's why it is so disappointing and embarrassing when he lets himself down," Taylor told the Press Association.
"We have to work hard on anger management now. We have trained counselors in this field and we will be offering their services to Liverpool and the player to try to improve matters."