The 30-year-old joined the Red Devils on the final day of the winter transfer window from Chinese Super League side Shanghai Shenhua on a deal that was supposed to run until May 31.
However, the Coronavirus pandemic has disrupted the footballing calendar around the world, leading to the suspension of the English Premier League.
Plans are in place to restart the EPL in the middle of June, meaning Ighalo’s deal would have expired by then unless Manchester United can renegotiate for an extension with Shanghai Shenhua.
The Chinese Super League, which was supposed to start on February 22 could return in late June or July.
Ighalo has enjoyed his time in Manchester so far, scoring four goals in eight games before the season was halted.
"I would like to finish the season if it's possible," Ighalo told BBC Sport.
"I was in good form, good shape, scoring goals and now we've stopped now for over a month. I've given it my best and hopefully we'll come back to play.
"The team had a good momentum before the pandemic started. At the moment I'm on loan, and this will cut short my time at the club."
"The club, myself, every footballer is going through a lot because we can't do what we love and what we know how to do best, so we're just thinking about that for now and to finish the season before we start thinking about the contract.”
"I just want everyone to be safe and see what the future holds."
