Footballers should "feel free" to protest over the death of George Floyd and "should take a knee", says Kick It Out chair Sanjay Bhandari.
The Football Association said it would take a "common sense approach" to any such protests.
Protests have been held in the USA after African-American Floyd, an unarmed black man, died after being restrained by Minneapolis police.
Bhandari said players taking a knee would be a "very powerful image".
"If they feel they want to protest, then they should. They should feel free to do that," he told BBC Radio 4's Today Programme.
Four players in the Bundesliga, including England forward Jadon Sancho, are under investigation for breaching rules over making political statements in games at the weekend. The same rules are in place in England.
"It's a fundamental human right to express your beliefs," Bhandari said. "My suggestion is that they should take a knee.
"I would say that taking a knee when you score a goal and have the whole team do it, the referee is not going to book an entire team. It's a very powerful image and a gesture of solidarity."
In a statement, the FA said it "strongly condemns discrimination of any kind" and that it has "endeavoured to ensure that football in England is both diverse and inclusive in recent years".
"Where any behaviours or gestures on the pitch that may constitute a breach of the Laws of the Game have to be assessed, they would be reviewed on a case-by-case basis with a common sense approach and understanding of their context," the statement added.
"The power of football can break down barriers across communities and we remain deeply committed to removing all forms of discrimination from across the game we all love."
On Monday, Liverpool players took a knee around the centre circle at Anfield during training, while Manchester United players Paul Pogba and Marcus Rashford added their voices to worldwide protests against racism. Newcastle and Chelsea players took a knee before their training sessions on Tuesday.Newcastle United's players took a knee at training in a picture posted by the club on Tuesday Chelsea players followed suit and kneeled in a H formation at Tuesday's training session
Floyd died on 25 May after being restrained by white Minneapolis police officer Derek Chauvin, who knelt on his neck for almost nine minutes to pin him down.
Chauvin has since been charged with Floyd's murder and sacked.
The FA's statement echoed one from world governing body Fifa.
In a statement on Tuesday, Fifa said it "fully understands the depth of sentiment and concerns expressed by many footballers in light of the tragic circumstances of the George Floyd case".
It added that applying the laws of the game was the responsibility of competition organisers, such as domestic leagues, who Fifa said "should use common sense and have in consideration the context surrounding the events".
The Commonwealth Games Federation wrote an open letter to sport, saying that what was happening in the US needed to be "a wake-up call" to athletes and administrators.
"Surely it is time for the world of sport to grant itself a social and moral licence," the letter signed by CGF president Louise Martin and chief executive David Grevemberg said.
"A licence to use all its platforms to encourage athletes, coaches, officials, sponsors, administrators and fans to inspire, to educate, to stand for what they believe in.
"A licence to provide the scope and freedom for all our participants to be agents of change, advocates of integrity and ambassadors for respect, impartiality and non-discrimination."
Kate Allen, director of Amnesty International UK, said: "We would applaud UK athletes who want to make a personal gesture of solidarity with Black Lives Matter campaigners in the US, or in the UK for that matter.
"While we don't expect all sporting stars to take a stand, we're encouraged that more and more are doing so. Given how influential sporting stars are, a well-timed solidarity gesture or public statement can be genuinely impactful."