That is according to former Chelsea defender Andy Townsend, who says that if Alexis Sanchez comes back firing then it gives them a great chance.
Manchester United have now won six consecutive Premier League matches since Ole Gunnar Solksjaer replaced Jose Mourinho as interim boss in December.
After suffering their worst ever start to a season in the Premier League era under Mourinho, the team are now playing the kind of football that fans expect.
And the improved run of form has now positioned them level on 44 points with Arsenal in fifth and just three points behind fourth-placed Chelsea.
“They haven’t even got Sanchez up to speed yet”
A few weeks ago the Red Devils looked a million miles away from a coveted top four spot that would qualify them for the Champions League next season.
But with the likes of Paul Pogba, Marcus Rashford and Anthony Martial now firing on all cylinders, doing just that is looking increasingly likely.
But Townsend thinks that they could even go one better than fourth if Chile international Sanchez comes back into the team with a point to prove.
“With the squad Solskjaer has got and the way they are playing I don’t think it is too much to say they can finish in a top three spot,” Townsend told Premier League.com.
“They haven’t even got Sanchez up to speed yet so if he can find his best game then things are looking very serious for Manchester United right now.
“They have always had the squad but just couldn’t knit it together but now you are saying what they can do.”
Sanchez has been a huge disappointment since arriving from Arsenal last year with rumours about his unhappiness at the club leading to speculation that he could leave.
The forward is the highest paid player at the club, reported to be on wages of a round £500,000-a-week.
But with Solksjaer now in charge, the hope is that he can reproduce the form he showed at Arsenal.
The 30-year-old has been out through injury over the festive period but could return for the next game for the FA Cup game against his former side on Friday.
Former Arsenal man Ian Wright agrees that a top three spot is not out of United’s grasp when you also take into account Tottenham’s current problems.
Spurs currently occupy third spot in the Premier League and are seven points ahead of United but are in the midst of an injury crisis.
All four of their top scorers this season are now missing after Dele Alli suffered a hamstring injury in the win at Fulham on Sunday.
Harry Kane, Lucas Moura and now Alli are all on the sidelines through injury while Son Heung-min is away with South Korea for the Asian Cup.
The four players have netted 40 goals between them in all competitions this season.
And this leaves the door open for Solksjaer’s men, according to Wright.
“When you think as well that Spurs have lost Kane for a while and Son has gone then you really start to think that United could finish in the top three.
United are next in action on Friday when they travel to Arsenal in the FA Cup fourth-round.