Celtic's opponents Shakhter Karagandy had already killed a sheep at the Astana Arena the day before last week's 2-0 first leg win over the Glasgow side.
Ahead of the return match, animal activists and the SSPCA urged police to intervene after manager Viktor Kumykov hinted that the ritual may be performed to help players "relax" ahead of the game.
He told a press conference that it would not be too hard to find a sheep in Scotland and that traditions should be respected.
The Russian, speaking through and interpreter, said: "All I can say is that every team and every club has its own pre-match traditions and rituals. Celtic must have their own. We will try to respect our traditions and those traditions have been in place even before we came to the club."
Asked if the ritual would take place, he replied: "Possibly, yes."
Then, when asked where he planned to get the sheep, Kumykov, to laughter, replied: "As far as we know in Scotland the agriculture is very developed so it shouldn't be an issue to find a sheep."
The Shakhter boss, though, played down the effects the pre-match ritual had on the first game in Kazakhstan.
He said: "Of course this tradition may have a certain psychological impact on players that can help them to relax before the game. But what really matters is on the football pitch, the game and the final score and you know we scored twice in the first-leg and Celtic failed to score, that's what really matters."
Following the press conference, John Patrick, spokesman for Scotland for Animals, said he would push for the arrest and prosecution of all involved under the Welfare of Animals at the Time of Killing regulations and the Animal Health and Welfare Act.
He added: "We appeal to Celtic and its fans to speak out against these animal sacrifices. It's an affront to the game."
Chief executive of animal protection charity OneKind, John Brady, said the arrogance of the side was "quite staggering".
He said: "It is quite clear there will be a backlash from this horrific practice, which has nothing whatsoever to do with football or sport. Surely it's not too much to ask for the visiting side to be respectful of people's views and feelings, not to mention strict laws on animal slaughter, while they are playing on our soil."
Police Scotland confirmed that, after discussions with the visitors, no slaughter would take place.
A spokeswoman said: "Police Scotland has been working closely with the clubs and there has been a lot of planning and preparation for the game. There will be no pre-match ritual that deviates from normal pre-match activity at Scottish games."