In December a group of the Russian club's fans published a manifesto calling for sexual minorities and non-Europeans to be kept out of the St Petersburg club.
Included in the Zenit fans' statement was the comment: "The absence of black-skinned players in Zenit's team is just an important tradition that underlines the identity of the club - and nothing more."
Two months ago QPR and former Anzhi Makhachkala defender Chris Samba labelled the Zenit fans racist and said they "are living in another century".
Liverpool, who have already 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 - in the squad.
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 haven't spoken to any of the players at the moment but we still have a few meetings to go," said the Reds boss, who insisted he never considered leaving any of his black players at home for the match.
"I will make reference to it because we have players it maybe could affect but we are here for football. We are very hopeful there will be a terrific game and anything that goes on outside the field will be taken care of.
"It is a social issue, not just a football issue, and it is something over the last 20-odd years that we as a football club and in Britain a lot of work has gone into outside of football to prevent racism.
"I know these are players who want to play and Glen is a very experienced, top international player. It is an issue these young players have experienced in their lives before. Obviously they understand and the likes of young Raheem has been through situations like this (in an Under-21 international in Serbia in October)."