The 17-year-old - who is yet to make his debut for Liverpool's first team - claimed on Thursday that Uefa "don't really care" about racism.
The FA said they wanted to collaborate closely with Uefa and world governing body Federation Internationale de Football Association over the issue.
In his interview with the Guardian, Brewster spoke about Gibbs-White being called a "monkey" in the Under-17 World Cup final against Spain, which England won with both Gibbs-White and Brewster on the scoresheet.
"I want to be by myself and left to think".
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Under UEFA's rules any player found guilty of making racial slurs can be suspended for a minimum of 10 matches.
Liverpool manager Jurgen Klopp underlined at a news conference on Friday that Brewster has the club's full backing.
"I don't think UEFA take this seriously", he added. "That is how it feels anyway, like it has been brushed under the carpet", he said. "If he needs help, we will give it to him".
'I'm really happy he is courageous enough to do what he did because it's such an important thing, ' said the German.
"I can't believe that people have these kind of thoughts still in their mind, it's so unusual in this world that is happens".
"It's quite interesting because I have been really long in this business and I've never faced a situation like that". We needed a 17-year-old boy to shout out, "here, it's still happening and it's happening all the time - I need help, we need help to stop it". That means to a lot of people that it doesn't happen but obviously it happens all the time.