The claims could be raised in Monday night’s first televised BBC leadership debate between Rishi Sunak and Liz Truss as the battle to succeed Mr Johnson at No 10 Downing Street heats up.
There appears to be significant support among party members against Tory MPs who forced him out earlier this month.
There is a possibility that more members could vote to sign the petition to keep Mr Johnson than not to vote for Mr Sunak or Ms Truss in the leadership election.
Tory members have been signing the petition calling for a confirmation vote on MPs’ decision to impeach Johnson at a rate of almost 2,000 a day since it was launched last week.
Anyone signing it is asked to provide their membership number when they sign up. Lord Cruddas said fake membership numbers are quickly found and their names are not counted.
The names are sent to Andrew Stephenson, the chairman of the Conservative Campaign headquarters in Westminster.
Lord Cruddas told The Telegraph how Johnson had personally invited him to lunch last Friday. The couple dined alone, although Mr Johnson’s wife Carrie arrived half an hour before Lord Cruddas left, carrying their daughter Romy in her arms and accompanied by the Johnsons’ son Wilf.
“Boris thanked me for my ‘Boris to the Vote’ campaign. He said he enjoyed following him and wished me well,” she said.
“He said he could understand members’ anger at what had happened. He said he wished he could continue as prime minister. He said he doesn’t want to resign.”
Asked by the peer if he would “wipe out” his resignation immediately with “a magic wand”, Mr Johnson replied: “I would erase everything that stops me from being Prime Minister in a second.”