Zenit were fined in 2008 after fans threw bananas and shouted monkey chants in a tie with Marseille and again in March 2011 when ex-Brazil international Roberto Carlos was offered a banana.
Liverpool, who have written to Zenit and Uefa about the potential problem, have travelled with three black players – England international Glen Johnson and teenagers Andre Wisdom and Raheem Sterling.
And although Rodgers will address the issue in team meetings he expects Uefa, police and the club to take care of matters in the Europa League last 32 first leg tie.
"I will make reference to it because we have players it could affect, but we are here for football," said the Reds boss, who insisted he never considered leaving any of his black players at home for the match.
"We are very hopeful there will be a terrific game and anything that goes on outside the field will be taken care of."
Rodgers is confident any racist abuse would not affect his players and added: "It is something which will very much unite them."