Only last week their rivals Manchester City became the first Premier League club to sign a £12m-a-season deal with Nexen Tyres.
A rule change that comes into effect at the start of next season allows teams to have a secondary sleeve sponsor.
Jose Mourinho's side are hoping to secure a £15m sponsorship deal
Manchester United wages: Which Red Devils star earns the most?
Tue, March 21, 2017
Express Sport runs through how much each Manchester United player earns per week, according to Total Sportek
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How much do Jose Mourinho's Manchester United players earn each week?
The report suggests the club have been in negotiations with several big-money brands and are now on the verge of agreeing a large contract with one of their existing sponsors.
An Old Trafford source told the paper: “The club expect this to be a huge deal. We think it will beat or match anything else in the league.
“The staff down in London are already on it. They seem to expect the deal to come from a partner we are already in with.
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Manchester United hope to have a sponsor on their sleeves for next season
Manchester United transfers: Most likely summer deals
Tue, March 28, 2017
Express Sport brings you the most likely Manchester United summer deals according to Betfair
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John Terry – 100/1
“Plenty of them have already expressed an interest. AON and DHL already pay out huge sums to have continued links.
“The smart money is one of them to increase their current payments but there is also interest from China and abroad.”