Chelsea prevented three people from entering the stadium for Thursday's Europa League quarter-final at Slavia Prague after a video appeared to show them singing an abusive song about Liverpool forward Mohamed Salah.
The group were apparently chanting "Salah is a bomber" repeatedly.
Liverpool said the video showed "vile discriminatory chants" and was "dangerous and disturbing".
Three of the six people in the video were identified and barred.
Chelsea are working to identify the other three, who did not turn up to the match.
The Metropolitan Police said it would seek to apply for civil football banning orders for anyone identified engaging in racist chanting.
Egypt forward Salah, who made 13 appearances for Chelsea before leaving for Roma in 2016, is a practising Muslim and has previously faced abuse about his religion.
The Stamford Bridge club, who are working with police and Liverpool, said the people concerned were an "embarrassment".
The individuals will face bans from the club if they are found to be season ticket holders or members.
The video was circulated on social media on Thursday, prior to Chelsea's match at the Sinobo Stadium in Prague. The Blues won the first leg 1-0 thanks to a late header by Marcos Alonso.
"This behaviour needs to be called out for what it is - unadulterated bigotry," said a statement from Liverpool, who host Chelsea in the Premier League on Sunday. "There is no place for this behaviour in football; there is no place for it in society.
"A crime of this nature has more victims than any individual it is aimed at and, as such, collective and decisive action is needed to address it."
Chelsea released a statement during their match, saying the club finds "all forms of discriminatory behaviour abhorrent".
"Where there is clear evidence of Chelsea season ticket holders or members involved in such behaviour, we will take the strongest possible action against them," it added.
"Such individuals are an embarrassment to the vast majority of Chelsea supporters, who won't tolerate them in their club."
Anti-discrimination organisation Kick It Out said: "It's not on the terraces, but it's still a disgrace. We don't want fans like that anywhere near our game."
There have been several high-profile incidents of discriminatory abuse in football over recent months.
- Racist chanting was directed at several England players during a Euro 2020 qualifier in Montenegro. The disciplinary case will be dealt with by European football's governing body on 16 May.
- Derby winger Duane Holmes and Wigan defender Nathan Byrne were targeted by alleged racist abuse in the Championship on Saturday.
- Watford captain Troy Deeney and defenders Adrian Mariappa and Christian Kabasele received alleged racist abuse on social media this week.
- Juventus' 19-year-old Italian forward Moise Kean suffered racist abuse from the stands during a match at Cagliari on 2 April - with team-mate Leonardo Bonucci's suggestion that Kean was partly to blame called 'laughable' by England forward Raheem Sterling.
- Manchester City's Sterling was himself allegedly abused at Chelsea in December, while Uefa is investigating a case of alleged racist abuse towards another England player, Callum Hudson-Odoi, during Chelsea's Europa League win at Dynamo Kiev on 14 March.