New England Women’s boss Phil Neville should be facing the possibility of punishment from the Football Association over "misogynistic and sexist" tweets, Kick It Out has said.
The anti-discrimination group also said it had "serious concerns" over Neville’s suitability for his new job.
The former England and Manchester United player has no previous experience of working in women’s football, and the FA surprisingly turned to him when a host of better-qualified candidates pulled out of the running.
Neville has been forced to apologise for a series of historic tweets, and the FA has previously taken retrospective action over such messages on social media.
Neville tweeted in 2012 that he did not expect women to have been reading his posts because they would have been busy "preparing breakfast/getting kids ready/making the beds".
Kick It Out chief executive Roisin Wood said: "In light of recent action taken in response to historical social media comments made by current football participants, the question must now be asked - will the FA be charging Neville for posting discriminatory comments on social media?"
She added: "We believe that if the FA wants to recover the confidence of the public, it must ensure that the concerns surrounding Phil Neville’s appointment are comprehensively addressed."
Neville appeared to delete his Twitter account, @fizzer18, after the comments came to light.
He is due to lead England Women in March’s SheBelieves Cup, the tournament in which the Lionesses last year beat the United States under the guidance of Mark Sampson.
Sampson’s sacking in September created the vacancy that Neville has now filled, but Kick It Out has doubts over whether the new boss is the right person to lead the team.
Wood added: "Kick It Out have serious concerns over a recruitment process that has resulted in the appointment of someone with no record of management or experience in women’s football, and are making representations to the FA to ensure the governing body is transparent and accountable for their decision."
He apologised on Wednesday, saying: "Following comments made a number of years ago I would like to clarify that they were not and are not a true and genuine reflection of either my character or beliefs, and would like to apologise.
"I am fully aware of my responsibilities as the England Women’s head coach and am immensely proud and honoured to have been given the role."
The Women’s Sport Trust and the Female Coaching Network have also questioned how Neville came to secure his new position, a high-profile role with a World Cup looming next year.