St Petersburg's Peter TV said that on Wednesday evening about 40 hooligans attacked a small group of Liverpool fans when they were coming out of a local bar, forcing the English to seek cover inside.
Security staff used baseball bats to disperse the hooligans before escorting seven Liverpool supporters to safety. No-one was seriously hurt, the report said.
Zenit assured Liverpool on Wednesday that visiting fans attending the game should feel safe after concerns were raised over racism.
"The club's personnel... have been working hard so that the players and fans alike would enjoy tomorrow's match," the Russian champions said in a statement on their website.
"Zenit have always condemned any form of racism. We hope our opponents share the same principles and tomorrow we all be treated to a great football match and passionate crowd support."
Zenit supporters have been notorious for racist chanting during home games while the city of St Petersburg is known to have a strong right-wing nationalist influence.
In December, Zenit's largest fan group demanded the club refrain from buying black and gay players following turmoil surrounding the acquisition of Brazil striker Hulk. The fans said they wanted more home-grown or European players in the team.
Local media reported that some 2,500 police were patrolling the area outside the Petrovsky Stadium ahead of the match.
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