Ighalo’s loan move from Shanghai Shenhua expires at the end of May – but United may be able to extend it after the season was brough to a halt by the coronavirus pandemic.
Solskjaer is monitoring Erling Haaland’s situation at Borussia Dortmund and is also working through a shortlist of other strike targets drawn up by the club’s transfer committee.
Moussa Dembele and Timo Werner are among those under consideration, while United have also been alerted to the uncertainty over Harry Kane’s Tottenham future.
But Ighalo is a cut-price option in a summer when Solskjaer is targeting Jadon Sancho, Jack Grealish, James Maddison and Jude Bellingham.
The Nigeria international has impressed during his loan spell, with four goals in three starts, while his contribution off the pitch is also valued by Solskjaer.
He could be available for around £15m – but would have to take a massive cut on his salary in China, which is believed to be £300,000-a-week.
And despite being a life-long United fan, he is open to returning to Shanghai when his loan expires.
“There is no offer on the table yet because the season is still on and I'm yet to finish my loan deal,” Ighalo told Elegbete TV. “I don't just take decisions alone in my life. I have a principle and I have a guideline for everything I do. I always pray to God to direct me.
“I have seen so many tweets about this. I have seen so many people going crazy, (saying) 'go back to China', some say stay with Man United.
“Have you seen me say a word? I don't have anything to say. When the season's finished and I get two offers from the two teams, then I will sit and think about it, pray about it and whatever God says I should do, I will go with that.”
FIFA have confirmed any deals due to expire this summer should be allowed to run until whenever the season can be completed.
With football in England suspended indefinitely United would ideally want to extend the 30-year-old’s loan before making a final decision on their transfer plans.
Ighalo added: “I came to Manchester United to play for a pay cut because I wanted to.
“So anything could happen, but I want the season to finish and my loan to finish. Then I will see everything I have.
“You don't just rush and do things: 'I'm going here, I'm going here'. I have to sit down and finish the season well, sit down with my agent, see what's on the ground: A, B, C, D, is on the ground. Okay we have to pick.”