It is being reported there is a push by some senior Conservative Party members in the UK to see Boris Johnson effectively made party leader unchallenged.
Britain's Daily Telegraph claims some cabinet ministers there want to avoid weeks of damaging attacks, by putting just the country's former foreign secretary's name forward to the final vote of party members.
He got the support of 114 MPs in the first round on Thursday.
The alleged plan is for the remaining candidates to drop out of the campaign next week and leave Mr Johnson, the leadership favourite, as the only one remaining.
It comes after Mr Johnson said on Friday that he thinks voters are frustrated by senior party members arguing in public, adding he does not want to see any more of it.
Candidate Rory Stewart, who only got 19 votes on Thursday, criticised the plan on Twitter, saying: "Please write to your MP if you think this is not a good idea and please RT [retweet] if you think anyone else might think this is not a good idea..."
Please write to your MP if you think this is not a good idea and please RT if you think anyone else might think this is not a good idea.... pic.twitter.com/sK0N3sQJqC
— Rory Stewart (@RoryStewartUK) June 14, 2019
The next round of voting is on Tuesday next week, where the field of candidates will be trimmed down even further.
British Health Secretary Matt Hancock dropped out of the running on Friday, after securing only 20 votes in the first ballot.
Meanwhile, former Brexit Secretary Dominic Raab has attacked Mr Johnson in the UK's Daily Telegraph, saying that the party did not need a leader who he feels is seen as part of the "privileged elite".
He said: "When you campaign in marginal seats, who can reach out and unite the working class vote and the middle-class vote?
"Are we going to be in a better position to do that with a candidate who isn't so easily caricatured as being from the privileged elite, with the son of a refugee, a grammar school boy who is offering tax cuts to most of those people on £15,000 as opposed to people on £50,000 and above?"
Mr Raab also said that Mr Johnson's reluctance to take part in the proposed TV debates showed he may not have the "mettle" to take on the country's top job, saying: "If you're not up for the TV debates and the test that provides, people will argue it's a barometer for what would happen if you get the job."
He added: "If you can't take the heat of the TV studios, what chance of taking the heat of the negotiating chamber in Brussels?"
Mr Johnson appeared to bow to increasing pressure to make a similar commitment by his rivals, pledging on Friday to participate in the BBC debate, scheduled for next Tuesday evening.
However, he will not take part in Channel 4's debate this Sunday.
All six remaining candidates will take questions from grassroots party members on Saturday in Westminster.
