The Tory MP said he was extremely grateful to the UK for deciding to leave the European Union before Mr Juncker's "nightmare" plans came into effect.
Speaking to Nick Ferrari on LBC, Mr Rees-Mogg said: "I’m just so glad we’re leaving and are getting out of the possibility of a United States of Europe, which has always been the plan of the Commission.
"If you look at the response of senior European leaders to Monsieur Juncker, I think he’s in cloud cuckoo land. I don’t think there’s any demand for this."
GETTY/LBCMr Rees-Mogg said Juncker's plans were a nightmare for EU member states
He said Juncker's proposals to expand EU powers were coming at a time of great in-fighting between the big wigs in Brussels and other member states unwilling to stand by EU orders.
Mr Rees-Mogg continued: "It’s happening at a point when the Commission is not only dealing with Brexit but also battling the Hungarian Government and the Polish Government.
"There are lot of tensions within the EU and I think a United States of Europe is Monsieur Juncker’s dream. But it’s everyone else’s nightmare."
During the live Q&A session, the Tory politician ridiculed Brussels' demands for a divorce bill, saying the UK owed nothing to the EU.
He said: "Under EU and UK law Britain owes no money, not a brass farthing."
Mr Rees-Mogg once again dismissed rumours surrounding his future as leader of the Conservatives, saying the country needed a "stable" leader to steer it Brexit Britain.
He said: "I'm completely backing Mrs May. No one serious thinks I'm a credible candidate."
His comments follow another harsh attack against Mr Juncker in the House of Commons where he said the UK could never regret the liberty it gained from Brexit.
He said: “No one ever regrets liberty. Mr Juncker does not understand our desire to rule ourselves according to our own democracy and never will.”