However, the Reform UK leader has not ruled out more informal routes to share power with other parties.
Speaking to BBC East Midlands on Wednesday, he said Reform had a “responsibility to work with the most pragmatic and sensible people to get things done”.
“We’re not saying that at a local level, there are not groups of independents, for argument’s sake, that we might be able to work with.”
Asked whether his party could enter into formal coalitions with Tories, he replied: “There’ll be no formal coalitions with anybody, there will be working relationships.
“We’ll maintain our independence, but of course, in the interests of local people we’ll do deals.”
National parties exercise various levels of control over groups of local councillors who wish to do deals to govern locally.
According to the party’s rulebook, Labour councillors require the approval of its ruling National Executive Committee before entering into local tie-ups.
By contrast, the Green Party of England and Wales says local groups are able to make the “final decision” on where and whether to share power.
The BBC has asked Reform UK and the Conservatives to clarify how they would authorise agreements to share power after the local elections.
The Liberal Democrats. who are in coalitions with other parties in councils around the country, have also been approached for comment.