The Red Devils are struggling under David Moyes and sit ninth in the Premier League after 15 matches, but the Brazilian believes they can still reel in their main rivals.
United travels to Aston Villa on Sunday seeking its first league victory in five attempts, having suffered back-to-back home defeats to Everton and Newcastle United.
But Brazil defender Rafael has not given up hope of finishing on top of the pile.
"The league table looks strange but we are not that far from fourth place," he said in quotes reported by The Daily Star. "If we get a good run going, I think we have a chance. We can do 10 games unbeaten – this is Manchester United. This club can always win games. It is not impossible for us to win the title. We just need a good run now – we have done it before. Our target is always to win titles – Manchester United is about winning titles."
The 23-year-old also has designs on representing his country at the 2014 World Cup, having earned two caps for the host nation.
He added: "Of course I expect to play for Brazil next summer. I play for Manchester United and I'll try to play as many games as possible here to make it. I am fit again and working hard. The last time I played for Brazil was at the Olympics. I haven't been picked for quite a long time and I haven't heard from our national manager, Luiz Felipe Scolari. I just need to do my job here. I think he's going to call when he thinks I'm ready to play."