But those claims have been disputed by Rebels chief executive Ross Oakley who expects Cipriani to see out his two-year deal with Super Rugby's newest franchise.
"He hasn't asked to get out of his contract," said Oakley.
"I've spoken to his manager who told me there's no truth in the fact that he's wanting to go to Bath."
Cipriani's first season in Australia has been plagued by disciplinary problems.
The 23-year-old's latest breach of the Rebels' code of conduct - breaking a team curfew three weeks ago - led to the club issuing a statement saying it had 'lost confidence' in their high-profile recruit.
Cipriani was dropped for his side's two-match tour of South Africa but Oakley insists the fly-half is attempting to put things right in Australia ahead of the Rebels next home game against the Stormers on June 3.
"He's keeping his head down and working hard," added Oakley.
"He's training here and has been working very hard while the boys have been away in South Africa, so we'll see how it progresses as time rolls by.
"He's doing all the things he's been asked to do as well as his training, so it will be how the team and team management see that once they get back."
Meanwhile, Bath have made it clear that Cipriani isn't 'top of their list' when it comes to recruitment.
Despite losing Butch James to a return to South Africa this summer, Bath chief executive Nick Blofeld admits plenty of questions would need to be answered if his side were to even consider signing Cipriani.
"Danny is a very talented player but we don't know what happened in Australia yet," said Blofeld.
"We didn't want to go off strategy and sign somebody at the last minute."