President-elect Donald Trump and his team said they are making progress toward a deal to keep Carrier Corp.'s factory in Indianapolis.

On Thanksgiving Day, Trump announced his efforts to keep the plant in the U.S. The negotiations are being led by Vice President-elect Mike Pence, governor of Indiana. The United Technologies-owned company announced earlier this year it planned to move the factory and its 1,400 jobs to Mexico, a plan that has since been criticized by both Trump and Pence.

@realDonaldTrump: I am working hard, even on Thanksgiving, trying to get Carrier A.C. Company to stay in the U.S. (Indiana). MAKING PROGRESS - Will know soon!

The deal would likely keep a workforce in the U.S. The company has made it clear that in order to remain competitive with other manufacturers of furnaces and air conditioners, it needs to lower its labor costs. Carrier confirmed Thursday that it has held discussions with the new administration.

@carrier: Carrier has had discussions with the incoming administration and we look forward to working together. Nothing to announce at this time.

Correction: Mike Pence is currently governor of Indiana. An earlier version misstated his status.

— CNBC's David Faber contributed to this report.