Qualification for Russia 2018 began on Thursday but Webb, who also serves as CONCACAF's president, believes FIFA will have to move the World Cup somewhere else if the Eurasian nation does not clean up its act.
According to the World Values Survey - an international network of social scientists - between 15 and 20 per cent of the Russian population answered "people of another race" when asked to pick groups they would not want as neighbours in 2013.
Webb confirmed this is a concern for FIFA, despite the fact football's global governing body selected Russia ahead of Portugal-Spain, Belgium-Netherlands and England in 2010.
"Definitely Russia poses a huge challenge for FIFA and the World Cup from a racism standpoint," Webb told ESPNFC.com on Thursday.
In September, Zenit St Petersburg striker Hulk was the subject of racist chants during a match against Spartak Moscow, while in 2013, Manchester City's Yaya Toure suffered similar treatment in a UEFA Champions League match away to CSKA Moscow.
In 2012, a Zenit fan group sent a petition to the Russian Premier League club demanding the St Petersburg-based outfit never sign "black players" or those from "sexual minorities".
Fare proposed a number of ideas to improve tolerance in Russian football but conceded "the opportunity to bring about long-term change [prior to the World Cup] may have passed".
"There's a lot of work there to be done from a educational aspect," he said.
"[Russia's] minister of sport [Vitaly Mutko], who is also on the FIFA executive committee, has acknowledged that, and I believe now they're going to put some plans in place to start to tackle diversity education programs.
"From our task force standpoint, we now have a dedicated staff who works with us on racism, and they're working very closely with Russia to implement and execute education programs.
"It's a huge opportunity to influence some change and we better influence some change over the next three years. We have to. We can't have a World Cup there under the current conditions."
