Eyebrows were raised when the former Watford striker made his deadline day switch from the Chinese Super League side in January, but the 30-year-old quickly made an impression at Old Trafford.
Ighalo not only helped ease the attacking burden, with Marcus Rashford sidelined by a back injury, but the lifelong United fan chipped in with four goals in three starts.
The coronavirus situation in China meant Shanghai Shenhua had been open to accommodating that loan deal, but the pandemic's subsequent impact in England means play will now go on beyond the loan's May 31 expiration date.
Ighalo's parent club have been reluctant to extend the loan as the Chinese season edges closer to getting under way, but Solskjaer has not given up hope on a deal being struck.
"The loan deal went to the end of May now, so obviously he's supposed to be going back," the United boss said.
"We're in dialogue and hopefully (he can stay). They've been great towards us, his club, and allow him to play for his dream club.
"It's been a dream for him and hopefully he can finish off what he started, maybe with a trophy or two.
"Hopefully now we've proved we can do this safely and we can move to the next step. It's been really enjoyable being on the training ground again.
"Everyone's looking sharp, everyone's been in with a good mood and we've been splitting up in groups so (working in) fours and fives together and they've really done well.
"Hopefully, they can as I said, step up and go to bigger training groups but so far it's been good."