Unless they win their final two games by improbably high scores, the Old Trafford outfit will not be able to catch leaders Manchester City if they overcome their last couple of opponents, Newcastle and QPR.
"We will keep fighting because there are two games left," he said.
"The possibility remains for us to win the title.
"Some people say the chance is very low. Some say they are high. But we will keep fighting until the end."
On Sunday, Phil Jones realises United cannot afford to be dictated to.
"Swansea do tend to have the majority of possession against teams but hopefully we can put that right," said the England defender.
"It is important in any game that we keep the ball and play at our tempo, the way we like to play.
"I am sure we will be able to do that."