The Red Devils recorded an emphatic 6-2 win against old rivals Leeds United at Old Trafford on Saturday to move up to third place in the table.
After a mixed start to the season, United have now won six of their last seven games in England’s top flight as they continue to gather momentum.
If they win their game in hand, they will be just two points away from league leaders Liverpool.
And former United defender O’Shea feels Ole Gunnar Solskjaer’s side will mount a title challenge but will need to be more consistent to close the gap on Liverpool.
‘So I’d have to say yeah they will be contenders, their form and goalscoring ability shows that.
‘And they have shown like they did against [Manchester] City that they can shut up shop too.
‘What they need to do to close the gap is get that consistency back.
‘If they get that consistency they’ll definitely be very close.’