Mr Zahawi sought to downplay the talks on Sunday and the suggestion that they were held in “secret”.
“She’s also the senior civil servant responsible for levelling up and making sure the United Kingdom gains the benefit in all its formations,” he told the BBC’s Sunday Morning.
“The Prime Minister meets his civil servants all the time.”
Mr Zahawi insisted he did not know who had called the meeting and that he did not believe any meeting was “material to the outcome of the investigation”.
“Sue Gray is professional, and has the highest level of integrity,” he added. “She is independent, the Prime Minister will never intervene, interfere, in the investigation.”
The BBC initially reported that the discussions touched on whether photos would be revealed to the public, and that Ms Gray initiated the meeting “to clarify her intentions” for what would happen once the police investigation concluded.
However, a spokesman for the inquiry disputed this account of events, while a No 10 source insisted the request for the meeting did not come from Mr Johnson.
It has also been reported that the meeting was suggested by a No 10 official, while the calendar invite was sent by Ms Gray.
It comes as about 30 people, including Mr Johnson, are being contacted by the Cabinet Office to warn them of the contents of the document ahead of its expected publication next week.
Most of the letters are believed to have been sent out on Thursday, as the Metropolitan Police concluded its investigation into lockdown breaches in Downing Street and across Whitehall.
Angela Rayner, Labour’s deputy leader, has called on the Prime Minister to “urgently explain” why the “secret meeting” with Ms Gray took place.