The 30-year-old Bayern Munich central defender has been linked with a January switch to Old Trafford and some reports had even claimed a deal was done.
But Dante has been quick to play down any such notion that he has agreed to leave Bayern and it is understood he is in talks over a new deal, with two years left to run on his current contract.
"What I can say is that my agents are the ones who handle deals and talks," he told Fox Sports Brasil.
"I am happy at Bayern and the most important is to keep working, I am happy with Man Utd's interest, let's see what happens in the future."
"I follow the Premier League and although Man Utd are in a bad moment, I appreciate the interest."
He concluded: "We have to wait until 31 January, a lot can happen in the future."
His agent Marcus Marin was also quick to rule out a deal with United.
"There is no agreement with Manchester United," he is quoted by the Independent.
"We are currently in negotiations with Bayern over a new deal and his first option is to play there.
"He is very happy in Germany at the moment but if nothing can be arranged in the next few weeks then of course he would have to explore his options elsewhere.
"Dante is at a crucial stage of his career so he needs to think about one last big contract. He has had a brilliant year and won several medals so we know how important the next few months will be.
"We are hoping that something can be resolved before the World Cup."
Marin revealed that United had previously been wanted by United, ahead of his move to Bayern.
"Manchester United followed him two years ago," Marin said. "We were in talks with them, but then he ended up at Bayern.
"They are a very good club - and a very big club - so it would be interesting if they were interested in Dante, although I stress we have not spoken to anyone."