The Nigerian joined on loan from Shanghai Shenhua last month and has travelled to London to face Chelsea on Monday.
And Solskjaer says there is always a chance Ighalo could remain at United if he impresses over the rest of the campaign.
“It’s a loan, but when you’re in the door and if you impress it gives you a chance,” said Solskjaer at his pre-match press conference.
“That’s exactly the same for everyone who signs if it’s permanent or it’s a loan. If you impress as a player, if you impress as a person, if you can help this group improve, then of course there’s a chance that we’ll look at extending things.
“That doesn’t just go for Odion, but since you asked, yes, of course his incentive is to play as well as he can. And it’s up to us to make sure that he’d want to stay if we wanted him.
“I think he’s probably pinching himself at times, because he’s now at his favourite club at the age of 30.
“Hopefully he’ll prove to you what I think he will. He’s a proven goalscorer, so he’ll do all right.”