United are attempting to extend the former Watford player's stay at Old Trafford, but a deal has yet to be struck with Ighalo's parent Chinese club, Shanghai Shenhua.
Manager Solskjaer wants to keep hold of Ighalo for if and when the Premier League season resumes, after he made a bright impact in the early weeks of his temporary switch to United.
Time is running out though, with Ighalo's short-term contract, agreed at the end of January, due to expire at the end of this month.
Solskjaer told MUTV: "The loan deal went until the end of May now, so obviously he's supposed to be going back.
"We're in dialogue. They've been great towards us, his club, and allowed him to play for his dream club.
"It's been a dream for him and hopefully he can finish off what he started, hopefully with a trophy for us.
"At the moment, nothing has been agreed. Their league is going to get started soon so we're just waiting to see."
Nigerian Ighalo, 30, supported United as a boy and has scored four goals in eight appearances for the club, netting in each of his three starts.
The Premier League season, suspended in March due to the coronavirus pandemic, could resume in June, but officials have admitted there is a chance the campaign may have to be curtailed.