The Red Devils lost 8-7 on penalties to Frank Lampard’s Derby County side at Old Trafford in the League Cup third round on Tuesday night.
Manchester United were held to a frustrating 1-1 draw with promoted side Wolverhampton Wanderers in the Premier League at the weekend.
The 20-time English champions have already lost to Brighton and Tottenham Hotspur to lose significant ground on their title rivals.
West Ham ended a losing start to the Premier League season with a 3-1 win at Everton before a goalless draw with Chelsea FC last weekend.
Former Manchester United striker Owen believes the Red Devils will either draw or lose at West Ham in the early kick-off on Saturday afternoon.
“West Ham have improved in recent weeks and could easily have taken all three points against Chelsea last weekend with Andriy Yarmolenko missing a gilt-edged late opportunity,” Owen told BT Sport.
“United were knocked out of the League Cup against an improving Derby County midweek, but their away form – won their last three – is, actually better than their home form at present.”
“It would not surprise me if the game finished all square, but if there is to be a winner I think the hosts might nick it.”
Manchester United haven’t won the Premier League title since 2013 when Sir Alex Ferguson was still in charge of the Old Trafford outfit.
The Red Devils will take on Spanish side Valencia at Old Trafford in the Champions League next week after Mourinho’s side were 3-0 winners against Young Boys in Switzerland.
The 20-time English champions finished in second spot in the Premier League table last season.
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