Downing Street commented that the Prime Minister is taking these claims “very seriously”.
The comments come after Ms Ghani said that her faith was given as a reason for her sacking as a minister in 2020.
The Conservative MP told the Sunday Times her “Muslimness was raised as an issue.”
A Number 10 spokeswoman said: “The Prime Minister has asked the Cabinet Office to conduct an inquiry into the allegations made by Nusrat Ghani MP.
“At the time these allegations were first made, the Prime Minister recommended to her that she make a formal complaint to CCHQ (Conservative Campaign Headquarters).
“She did not take up this offer.
“The Prime Minister has now asked officials to establish the facts about what happened.
“As he said at the time, the Prime Minister takes these claims very seriously.”
Conservative Chief Whip Mark Spencer says the claims are completely false. He has said Ms Ghani was referring to him and he considered her allegations defamatory.
Mr Spencer said: “I have never used those words attributed to me.
"These claims relate to a meeting in March 2020. When Ms Ghani raised them she was invited to use the formal CCHQ complaints procedure. She declined to do so.”
Speaking on Sunday, Ms Ghani said she did not use the internal Conservative Party complaint process when previously invited because it was “very clearly not something that happened on Government business.”
Education Secretary Nadhim Zahawi told Sky News: “She has made a very serious allegation, the Prime Minister spoke to her last night and said the Cabinet Office will investigate this and look at the detail of this.
“She put out a statement last night saying actually, to be fair to her, this could be people who weren’t even members of the Conservative Party, which is why we need to get to the bottom of this very quickly.
“And of course the Chief Whip (Mark Spencer) has come out and named himself as the individual and I work with both colleagues, and I think it is important that someone like a Cabinet Office senior civil servant should look at this properly, because the Chief Whip has also categorically denied this.”