The allegations stem from leaked emails published by the Daily Mail which appear to show Henry ruling out the possibility of signing players of African descent during the January transfer window.
Henry's comments came from an email sent to another senior West Ham official and an agent on January 27 when discussing a footballer of Cameroonian descent.
"We don't want any more Africans and he's not good enough. I sent Thomas to watch him and the other lad last week and he said no. If Palace take them good luck," read the initial email, according to the Daily Mail.
Henry was then asked whether there was a club policy regarding African players, which he denied only to then be informed that he had told more than one agent during the January transfer window that the club did not want any more African players.
Henry then confirmed that was the case, saying: "Yeah. Because we had three and we felt we didn't particularly want any more African players."
When asked why the Hammers were reluctant to add to their African contingent, Henry added: "Erm, no reason. It's nothing racist at all. It's just sometimes they can have a bad attitude.
"We had problems with Sakho, with Diafra Sakho. We find that when they are not in the team they cause mayhem. It's nothing against the African race at all.
"I mean, look, there are top African players. There's not a problem with them. It's just sometimes they cause a lot of problems when they are not playing, as we had with Diafra. He's left, so great. It's nothing personal at all."
It was then put to Henry that his views were discriminatory against African players, but the Hammers director rejected that assertion, saying: "No. I don't know what you are trying to get at here. All I said was, look, we have a great lad in [Cheikhou] Kouyate, he's brilliant, a great player for us, he's a good lad.
"But the likes of Sakho have caused mayhem. When he's not playing ... he always wants a new deal. That's all it was. It was nothing discriminatory at all. I could say we get offered Russian players. I just find with Russian players that they don't settle in England.
"It's like Italians. How many Italians come and settle in England? As a club we are not discriminatory at all. If you've got too many, they all sit together and it becomes a situation where you can have problems. But then you can have problems with English players. I don't know what you are driving at."
The chairperson of Kick It Out Lord Ouseley has since described the exchange as "unacceptable" and "unlawful"