This is despite being charged with misconduct by the Football Association over comments he made about African players earlier this year.
Henry, who had a long playing career, was suspended by the Hammers before being sacked in February after he was accused of racism and discrimination for allegedly telling agents the Premier League club did not want to sign any more African players.
It was reported he had said in an email that West Ham wanted to limit the number of African players because they “sometimes have a bad attitude” and “cause mayhem” when they are not in the team.
Those comments were deemed “unacceptable” by the club, while the Professional Footballers’ Association said it was “shocked” by the report, and the FA has since charged Henry, a former Shrewsbury Town midfielder, who spent the 1991-92 season at Gay Meadow.
He has denied being racist and claimed he had received messages of support from African players.
In an interview with Sky Sports News he said he had been offered a player by an agent, before adding: “I went back (to the agent) and said, ‘We don’t want any more Africans and the player isn’t good enough – my scout has said the player isn’t good enough’.
“I hold my hands up, I was totally wrong. I shouldn’t have said it. But I do think it was taken completely out of context.
“It was never, ever meant to be racist in any way.
“The reason we said we didn’t want any more Africans was because we already had three – the day before we’d had four but one of them left.
"And I just felt that as the head of recruitment I look ahead down the line, and I thought ‘In 12 months’ time it’s the African Nations Cup – if we had four African players come the next African Nations Cup we’re going to lose them in January/February and we could struggle with that’."
He added: “I’ve had messages from three or four of the players and I’ve had messages from a lot of people in the game and a lot of African descent, saying basically ‘We’re right behind you mate’, and they know I’m not a racist.
“What I said was wrong. I’ve been sacked by West Ham, I’ve been at home for three months. I don’t know what it’s going to be like to get back into work but I am not racist in any shape or form.”
After charging him last week, the FA said in a statement: “Tony Henry, former West Ham United FC head of player recruitment, has been charged with misconduct in relation to comments he made which are alleged to be improper and/or insulting and/or abusive.
“It is further alleged that this breach of Rule E3(1) is an “aggravated breach” as defined in Rule E3(2), as it included reference to ethnic origin and/or race and/or nationality and/or colour. Mr Henry has until May 15, 2018 to respond to the charge.”
West Ham have six first-team squad members of African descent in Cheikhou Kouyate, Pedro Obiang, Joao Mario, Angelo Ogbonna, Arthur Masuaku and Edimilson Fernandes.
Senegal striker Diafra Sakho left the club in the January transfer window to join Rennes, with Ghana international Andre Ayew heading to Swansea.