Rishi Sunak has hinted that Nigel Farage could be welcomed back into the “broad church” of the Conservative party – only for the former Ukip leader to say he was not interested. Farage has been conspicuous at the Tory conference in Manchester this week, where he is broadcasting for GB News, including a singalong with Priti Patel on Monday evening. Farage was a Conservative party member but left in 1992 over the signing of the Maastricht treaty. However, a possible return has been questioned after Brexit. Asked by GB News if this could happen, Sunak refused to rule it out, saying: “Look, the Tory party is a broad church. I welcome lots of people who want to subscribe to our ideals, to our values.” When asked if this could include Farage, Sunak avoided the question, saying: “The thing I care about is delivering for the country and the more people as we’ve seen at this conference – we’ve had record attendance I think at this conference. Lots of energy, lots of engagement.” Jacob Rees-Mogg, the former Commons leader and business secretary, told the BBC he would back the idea of Farage rejoining, calling him a “very effective campaigner” with whom he shared “most of his political views”. Rees-Mogg said: “I think Nigel is broadly a Tory and always has been. If he wanted to join I can’t think his membership would be refused.” Speaking at a subsequent fringe meeting, Rees-Mogg said Farage should be made a Conservative peer, adding: “The problem is if he became an MP I think any leader of the party might be looking quite nervously behind his back.” But speaking later to GB News, Farage rejected the idea – while Greg Hands, the Tory party chair, also said he would be unlikely to get admitted anyway. Asked if he might join the Conservatives, Farage said: “Would I want to join a party that’s put the tax rate up to the highest in over 70 years, that has allowed net migration to run at over half a million a year, that has not used Brexit to deregulate to help small businesses? No, no and no.” He added: “I achieved a lot more outside of the Tory party than I ever could have done from within it.” Hands told the BBC: “I think he’s been most recently advocating voting for another political party. That is not consistent with being a member of the Conservative party.” Asked if he would welcome Farage, Hands said: “No, I don’t think I would because I think he’s repeatedly for the last 30 years or more advocated voting for other political parties. I think he said he doesn’t want to see the Conservative party succeed so I don’t think I would.” Farage remains notably popular with parts of the Tory right, and attended Monday’s conference fringe speech by the former prime minister Liz Truss. That night, he was filmed at a GB News party dancing with Priti Patel, the former home secretary, as they both sang along to Can’t Take My Eyes Off You. Farage would, however, be deeply unpopular with other elements of the party, in part because of his regular criticism of the Tories, but also because of his record of supporting contentious populist views and being linked to antisemitic conspiracy theories. He has repeatedly used terms associated to such ideas, and was interviewed numerous times by Alex Jones, the US far-right conspiracy theorist, who was sued successfully by bereaved parents for claiming a US school shooting was faked.