The American car manufacturer signed a £450 million deal with the Premier League giants in 2012, which is due to end in 2021.
Since Sir Alex Ferguson left the club as Premier League champions in 2013, United have failed to win another league title.
They have won the FA Cup, the League Cup and the Europa League in that time, but failed to qualify for the Champions League last season.
The report claims that insiders believe parent company General Motors is very unlikely to extend its agreement with the club because they feel they overpaid for the rights seven years ago.
That suggestion is backed up by the fact that the executive who brokered the deal left the company soon afterwards.
However, the Old Trafford outfit insist they are still in a strong commercial position despite the struggles of their team.
The club announced a club record revenue of £627.1 million for the year ending 30 June 2019 – a 6.3% rise on the previous year.
But United’s commercial team have been looking for a new shirt sponsor for a while according to the newspaper, with several leading brands said to be interested in tapping into the club’s estimated 1.1 billion global fan base.
Ole Gunnar Solskjaer’s side have begun the 2019/20 campaign in bad form, hovering just two points above the relegation zone after picking up nine points from their opening eight games.
A club spokesperson told the outlet: “Chevrolet is a fantastic partner. The sponsorship continues to achieve the brand and business objectives for both parties and we will continue to work to activate and maximise it.”
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