The 30-year-old striker moved to Old Trafford on a six months loan deal in late January from the Chinese based club.
Football activities in England have, however, been suspended since March due to the coronavirus pandemic, and with many fixtures still to be played, the league season will continue past the expiration date of some player contracts, meaning there is uncertainty over the duration and renewal of contracts.More news: Record drop in energy investment, warns IEA think-tank
However, as a condition of him being allowed to extend his stay at Old Trafford, Ighalo is expected to sign a new deal with them.
A Nigerian worldwide, Ighalo has scored 16 goals in 35 games for his country, and played in the 2018 World Cup in Russian Federation.
Shanghai have been reluctant to sanction an extension but negotiations are ongoing.
"The loan deal went until the end of May now, so obviously he's supposed to be going back", Solskjaer told MUTV on Tuesday.More news: Billion Vaccine Adjuvant Doses Promised
While the former Watford striker wanted to make his stay in Manchester permanent, reports suggest that the stars have not aligned for the player after his parent club indicated they want him fresh for the new season.
"It's been a dream for him and hopefully he can finish off what he started, maybe with a trophy or two. We're just waiting to see".
Shanghai Shenhua are believed to be ready to bring in a short-term replacement for Ighalo should he not be able to return, giving Manchester United a boost in their attacking department for the coming months.More news: Trump Renews Promise to Withdraw US Troops from Afghanistan