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.
And The Sun claim Manchester United are set to trump their rivals with a bigger deal ahead of the next campaign.
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.
“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.”
