The Red Devils are currently up for sale, but are desperate to keep hold of their in-form striker whose contract is up at the end of next season.
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Rashford is currently having a fine campaign, having netted 27 goals in 44 games in all competitions.
According to The Sun, United are expected to enforce a wage cap on £200,000 per week for new deals.
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The report adds, though, that the 27-year-old is keen to wait until after the potential takeover from Qatar's Sheikh Jassim or Ineos owner Sir Jim Ratcliffe goes through.
Both are frontrunners to buy the club having been granted an extended deadline of 9pm on Friday, but neither will pay over the odds for the Old Trafford side.
Jassim and Ratcliffe, the latter who is the richest man in Britain, have both insisted they are prepared to spend big with the aim to get the club back where it belongs.
Rashford, therefore, is keen to hold off from signing a new contract for the time being, suggesting he is eyeing a deal greater than the proposed £200,000 salary cap.
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According to The Daily Mail: "This £200,000 per week clause won't apply to Rashford because he's on a higher salary at the moment and is unlikely take a pay cut."
Rashford was expected to be part of Gareth Southgate's squad to face Italy in Naples, but withdrew from England duty due to injury.
The forward, who has netted 18 goals in 25 games since the World Cup in Qatar, has recently been spotted in New York, taking a break away from the footballing scene.
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No matter who will purchase United, they will certainly want Rashford part of their project and will be prepared to do whatever it takes to keep hold of him.