Parliament had to “find a route” to deliver Brexit, he told Mr Farage during an appearance on his LBC radio show “which is why I want to make an offer to you.”
“You represent such an important part of this debate,” he said.
He added: “The fact you actually lead us out of Europe in the first place puts you in a very important position in this. We need to find a way, as a party, of reaching out to you. Not only to you, I also want to reach out to trade unions and other people in this country who care our economy … but we must reach out to you and bring you in to try to work out how we crack this.”
Mr Stewart said he was frustrated with his fellow Tory leadership candidate Boris Johnson because "he just keeps asserting again and again that he’s going to leave on October 31st and he never tells us how he's going to do it.”
Appearing to be momentarily taken aback, Mr Farage replied: “Well, Rory, interesting. I tell you, when it comes to getting us out of the European Union, and getting us to be sovereign country, I would meet with anybody and I’d travel anywhere to do that.”
Mr Farage had earlier said there was something wrong with the idea of a second referendum after 52 per cent of voters backed Britain’s exit in 2016.
Mr Stewart said: “You are completely right Nigel – I agree with everything you’ve said there. That referendum result should be respected.”
The Tory candidate said the EU would not re-open negotiations and said the idea – promised by Mr Johnson and other leadership rivals – was “totally for the birds”.
— Rory Stewart (@RoryStewartUK)June 16, 2019
Earlier on Sunday, Mr Stewart claimed Mr Johnson’s plans for Brexit would “come off the rails” once subjected to detailed examination.
He said his rival’s reluctance to submit to media scrutiny was undermining trust in politics.
“How is Boris going to deliver Brexit? He keeps saying “I am going to deliver it”. I don't even know what he believes. He won’t talk to me. He won’t talk to you. He won’t talk to the public,” he told BBC1’s The Andrew Marr Show. “We want to know what he believes. The real problem with politics is a problem of trust.”