The Red Devils sit seventh in the league, eight points off Arsenal in fourth and the two sides will meet on Wednesday.
United have not won since 3 November and drew their last two league games against Crystal Palace and Southampton.
Speaking to Brazilian outlet RedeTV after the 2-2 draw at St Mary’s, Mourinho said: “Last year, we said that getting in 2nd place was a fantastic thing due to the qualities we had compared to the qualities of the other teams fighting for the top four.”
Referring to his ambitions for the rest of the campaign, he said: “Try to win as many points as possible and try almost the miracle to end in fourth.”
Meanwhile, Mourinho is acting like he wants to be sacked, according to Chris Sutton.
Mourinho’s relationship with his players has come in for intensive scrutiny for much of the season and was under the spotlight again in the wake of Saturday’s draw.
Speaking on Radio 5 Live, former England striker Sutton said: “Mourinho is a better watch than Man United at the moment – the team on the pitch. Mourinho does more point scoring off the pitch than his team does on it.
Mourinho believes it will take 'a miracle' for Manchester United to reach the top four ( AFP/Getty)
“It’s not a happy camp. What’s going to happen in January? Can he be trusted with a pot of money in January?
“I think he wants the sack.
“His signings have been a disaster and he wants more money. How can they trust him with the performances the way they have been? What is good about Man United this season? And it all comes from the manager who is blaming everyone else.”