The Nigeria international joined United on loan in the January transfer window and has scored four times in eight appearances for the Red Devils in all competitions.
Ighalo's current deal in Manchester is due to expire on Sunday, but the 20-time English champions are allegedly determined to keep the centre-forward for at least the remainder of the 2019-20 campaign.
According to Goal, Ole Gunnar Solskjaer's side are continuing talks with Shanghai as they attempt to thrash out an agreement before the striker is due back in China.
The report claims that the two clubs could even strike a deal to allow the 30-year-old to stay with United until January 2021.
Ighalo, whose existing deal with Shanghai is due to run until December 2022, is allegedly willing to put a proposed £75m contract in jeopardy by pushing to remain in England.