The Nigeria international signed a short-term deal with the Old Trafford club in January and has exceeded expectations.
Ighalo scored four goals in his first three starts before European football was put on hold due to the coronavirus outbreak.
Sky Sports News has reported that the 30-year-old will be offered lucrative new terms by his Chinese parent club.
However, his loan spell at United is likely to be extended until June 30, rather than the originally agreed date of May 31, because of the coronavirus-enforced league suspension.
Shanghai want to tie Ighalo down for an extra two years, taking his contract expiry date from December 2022 to December 2024.
The former Watford striker is understood to be flattered by the offer but wants to delay a decision in case he is offered a permanent contract by the Red Devils.