Zenit supporters had published a document in December which stated they did not want the squad to contain any non-white or homosexual players. Liverpool travel to Russia on Thursday for the first leg of their last 32 clash with Zenit and Ayre insisted the club will work with the relevant authorities to make sure the players are protected.
"We'll take the right action," he told liverpoolfc.com. "The referee would be at the forefront of that if there's something on the pitch. Anything that happens off the pitch, then we'll work very closely with the authorities."
Ayre added: "Those authorities will be UEFA, who are sanctioning and hosting the match, and Zenit and ourselves. I'll be there at the game and I'll ensure that we do whatever we need to do to protect anything that happens to any of our players. We'll ensure that happens."
Ayre went on to say the threat of racist behaviour has been a concern to the club and revealed he has already been in contact with both UEFA and Zenit and remains "hopeful" that the tie will pass without serious incident.
"It's been a major concern for us," he added. "I wrote to UEFA very recently expressing our concerns to them - and also to Zenit themselves. We await some responses in that regard.
"The most we can do is make our feelings clear ahead of the game, and hope that we get an adequate response and adequate support on the night. That's about the most we can do at this stage. I'm certainly hopeful that the right people will take the right action to ensure it's a game where we don't have that type of incident."
Liverpool's players will be briefed before the game on Thursday about how the club would like them to respond to any abuse. Ayre believes walking off the pitch, like AC Milan midfielder Kevin-Prince Boateng did after being racially targeted during a friendly match last month, would not be something he would want to see from Liverpool's black players.
"We do plan to speak to the players about it," he said. "The most important thing for our players is that they remain professional throughout this. We certainly won't tolerate that type of attitude or any of those types of incidents from our team. So the important thing is that we let them know how we expect them to act if there is an incident.
"I'd much rather we take the incident off the pitch and we deal with it. Obviously the referee has a role to play within that. But we'll be briefing our players on what's acceptable and what's not."
- Sports & Recreation