Current frontrunner Boris Johnson did not make an appearance.
The report follows comments by the head of the UK Conservative Party's biggest donor group, who said that the country's next prime minister "needs to be willing to work" with Nigel Farage, an outspoken Eurosceptic and founder of the Brexit Party.
"I think there is a growing feeling in the party that when we get to the final two we should have a robust debate between two credible change candidates", he said.
UK PM hopeful Rory Stewart, who now serves as the worldwide development secretary, was among those who personally reached out to Farage, telling him on an LBC radio phone-in that the Conservative Party had to "find a way, as a party, of reaching out to you and bring you in to try to work out how we crack this, how do we get this [Brexit] through parliament".
"The difference between me and Boris is that I would try for a deal", said Foreign Minister Jeremy Hunt, who is placed third favourite in the leadership contest.
Rory Stewart, who wants to rule out a no-deal Brexit, took issue with the argument of Mr Johnson and other candidates that the only way to get an improved deal from the European Union was to prepare for leaving without an agreement and use that as leverage.
Brexit has claimed two prime ministers.
Nearly three years since Britain voted to leave the European Union, the country, the parliament and both main parties are still deeply divided over Brexit. "The European Union knows no deal can not get through parliament", said Stewart, a relative unknown who has shot up the bookmakers' odds to be placed second.
The media outlet cited a businessman familiar with the negotiations as saying that they were "very preliminary" and noting "you have to get Boris [Johnson] on board and that is going to be very tricky" until or if he's elected Tory leader.
"Who is going to be nimble enough, who has the style, who has the approach, who has the way of dealing with the public - I don't think the answer is going to be pre-scripted answers", he said. I was tempted like Michael and like Dom to say, 'believe in the bin!
The MP also defended Mr Johnson's decision not to take part in a debate on Sunday with the others left in the race - Jeremy Hunt, Michael Gove, Dominic Raab, Sajid Javid and Rory Stewart. "I certainly think the Conservatives can not win an election unless we've delivered Brexit".