Chief whip Mark Spencer, whose role it is to keep MPs on board with the government's agenda, took the unusual step of identifying himself as the person at the centre of the claims, and denied the allegations.
"These accusations are completely false and I consider them to be defamatory," he wrote on Twitter.
"I have never used those words attributed to me. It is disappointing that when this issue was raised before Ms Ghani declined to refer the matter to the Conservative Party for a formal investigation," he added.
The government whips are in the spotlight at the moment after they were accused by Tory MP William Wragg of "blackmailing" critics of under-fire Prime Minister Boris Johnson in order to prevent them from trying to oust him.
Ghani, vice-chairwoman of the influential 1922 Committee of Tory backbenchers, told the paper that "it was like being punched in the stomach. I felt humiliated and powerless."
She said she remained quiet for fear of being "ostracised by colleagues". Vaccine minister Zahawi demanded an investigation.
"There is no place for Islamophobia or any form of racism in our @Conservatives party," he tweeted, calling Ghani a "friend, a colleague & a brilliant parliamentarian."
"This has to be investigated properly & racism rooted out." Justice minister Dominic Raab called it a "very serious claim" but told BBC's "Sunday Morning" that there would only likely be an investigation if Ghani made a formal complaint, which she has so far not done.
Former equality and human rights commissioner Swaran Singh carried out an inquiry into claims of Islamophobia in the Conservative Party two years ago.
He analysed 727 separate incidents as recorded between 2015 and 2020 and found no evidence of "institutional Islamophobia", but criticised senior Tory figures including now prime minister Johnson.