As things stand, the Red Devils are Manchester City’s main threat to their fourth placed spot.
City are currently four points clear of their local rivals, but United have a game in hand and are in far superior form.
Louis van Gaal’s side take on Norwich City this weekend, while City face a tough match against Arsenal.
If United win and City lose, which is distinctly possible, the Red Devils will become favourites to claim a Champions League qualification spot, but there is an added complication as West Ham United are also in the mix.
That match could have huge consequences in the race for the top four, and Keown has suggested that he believes West Ham may well come out on top.
“They have a game in hand but it’s against West Ham in their last ever match at Upton Park,” the former Arsenal defender said. “If you look at the emotion stirred at Stamford Bridge on Monday then saying goodbye to Upton Park is going to be just as emotional.
“There will be generations of fans there who have enjoyed the Upton Park experience and it will be the last time to capture that. It’s a ground that has thrived on its reputation to reach fever pitch so they will give it a great send off, especially given the calibre of the opponent. I think that match could well spell the end of United’s chase for the top four.”
If West Ham do beat United, and City lose to Arsenal, then Slaven Bilic’s chances of breaking into the top four could still be alive.
West Ham are likely to have to win all three of their remaining fixtures - which come against Swansea, United and Stoke City - to have a chance of breaking into the Champions League qualification spaces.