The Red Devils have used the American car company as their main sponsor on their kits since the start of the 2014-15 season after agreeing a huge deal worth around £450m in 2012.
The seven-year agreement, thought to be worth a staggering £64m each year, is still the biggest shirt sponsorship deal in world sport.
However, with the contract due to expire in 2021 and Chevrolet believed to be looking for an early exit, The Sun claims that United are nearing a deal with the Haier Group.
According to the publication, executives from the Premier League club have held several talks with the Chinese company about featuring one of their brands on their shirt in place of their current sponsors.
Despite recent struggles on the pitch under Ole Gunnar Solskjaer, Haier are understood to have not been put off and retain significant interest in completing a deal.
Although club declined to comment, it is claimed that senior representatives of the company have held talks at United’s London base over the last few days – with Old Trafford bosses believed to want £70m-per-season.
The Sun reports that the two parties are nearing an agreement, but that the Red Devils are still open to considering other offers.
United have picked up just 17 points from their first 13 league games and are ninth in the table – nine points outside the top four – but the club are still considered a big commercial attraction.