Several Red Wall MPs are reportedly preparing to submit their letters to SIr Graham Brady.
The media mogul reportedly asked Johnson to scrap the BBC while bouncing the PM's son Wilfred on his knee at Chequers.
The prime minister insisted "nobody told me that what we were doing was against the rules".
Writing in the Telegraph, Moore said the BBC had failed to show "superimpartiality" in its Partygate coverage.
But the former foreign secretary said "It would take a lot to persuade me to put my hat into the ring".
It comes as new polling shows the chancellor holds a 28-point lead over Liz Truss among Conservative members.
"I moved to England because of its tolerance and open-mindedness. So when I started to see the posters on the windows, when I started to hear Nigel Farage demonising the foreigners, the hatred and racism that was now in plain sight, I started to feel uncomfortable."
The prime minister - now implicated in the inquiry - is effectively Sue Gray's boss!
Raab said lying to the Commons would "normally" be "a resigning matter" under the ministerial code.
TheLondonEconomic.com – Open, accessible and accountable news, sport, culture and lifestyle.
Read more
We do not charge or put articles behind a paywall. If you can, please show your appreciation for our free content by donating whatever you think is fair to help keep TLE growing and support real, independent, investigative journalism.
Editorial enquiries, please contact: [email protected]
Commercial enquiries, please contact: [email protected]
© The London Economic Newspaper Limited t/a TLE thelondoneconomic.com - All Rights Reserved. Privacy
© The London Economic Newspaper Limited t/a TLE thelondoneconomic.com - All Rights Reserved. Privacy
© The London Economic Newspaper Limited t/a TLE thelondoneconomic.com - All Rights Reserved. Privacy