The Liverpool star made headlines this week when he appeared to bite the shoulder of Italian defender Giorgio Chiellini during Uruguay’s 1-0 win over the Azzurri - an incident that the 27-year-old was not sent off for.
Suarez has bitten an opponent on two separate occasions previously - he was punished for sinking his teeth into PSV Eindhoven's Otman Bakkal in 2010 before being banned for biting the arm of Chelsea's Branislav Ivanovic in 2013.
Fifa have now confirmed that they have opened disciplinary proceedings into this week's incident, and if found guilty of the offence again, Suarez could be suspended for between three and 24 international matches or be given up to a two-year club and/or country ban.
And Zyryanov admitted that while Suarez should be banned, Fifa should only take the necessary action after the end of the World Cup in Brazil.
"I would allow him to play the rest of the World Cup. But then he must be punished,” he told Sport-Express.
"He already has previous incidents like this, with Branislav Ivanovic who he bit and [then] got a ban for 10 matches [as a result].
"They say off the pitch Suarez is fine, but in the heat of the match his emotions go wild.
"God has shown me mercy [for never being bitten]. I've been pushed, beaten off my feet, but biting? Thank God, that has not yet come into anyone's mind."
Fifa began proceedings into the incident on Wednesday and are likely to conclude discussions by the end of Thursday.
"We have to resolve it either today or tomorrow," Martin Hong, a member of Fifa's disciplinary panel, told reporters on Wednesday. "It's our duty to see justice done."
Should Suarez decide to appeal any ban given by the governing body, Fifa may have to take the case to the Court of Arbitration for Sport to reach a binding verdict before Uruguay's next World Cup match against Colombia on June 28.
But if Fifa were to ban the forward for fewer than three matches or only up to two months, Suarez would not be able to appeal as per the organisation's rules.