The Brazilian believes he has a better chance of winning silverware at the German side than at Old Trafford.
The Brazilian defender was reportedly a target for Louis Van Gaal’s side as he looks to bolster his defence, an area of the team that is particularly short on quality.
It is believed that United were willing to table an offer in the region of £20m for the 31-year-old, who was a key player in his country’s run to the World Cup semi-finals last year and a regular performer in Pep Guardiola’s side.
He has, however, turned down a move to Old Trafford, having suggested he stands a better chance of winning silverware with Bayern.
“I've been in at least the semi-finals of the Champions League and the German Cup in each of these three years, and won the Bundesliga each time,” Dante told the official Bundesliga website.
"It can hardly get any better than that."
The rejection from Dante could push United into looking to sign another Brazilian defender instead, Atletico Madrid’s Miranda.
The Telegraph has linked the Reds with a move for the centre-back, with Premier League rivals Chelsea also reportedly interested in him. With his contract set to expire next season, it is thought he could be secured for a relatively low fee - a big selling point to both clubs.