The Red Devils forward has entered the last 18 months of his contract and manager Erik ten Hag is desperate to keep him now he is embodying the player fans expected him to become when he broke through to the senior team.
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"Of course [Rashford's new contract] is a priority," Ten Hag said ahead of the clash against Leicester. "We are working on that, just sit and wait, but in the background we work hard. Of course [we have to keep him]."
Following his two goals against the Foxes on Sunday, the 25-year-old has now netted a mammoth 24 times already this season as well as recording eight assists in all competitions.
That tally has already smashed last year's total of five goals and two assists.
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Last month, talkSPORT brought you the news Rashford is expected to sign a new contract with the club he's been at for his entire career.
Now, ex-Crystal Palace owner and White and Jordan co-host Jordan has advised the Man United star to dedicate his future to the club, considering they stood by him during his struggles last season following his penalty miss in the Euro 2020 final.
"If he's got any integrity - which is a word that doesn't often belong in football - he should be signing a new contract with Man United because they've been carrying him for 18 months," he told talkSPORT.
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"He didn't do anything for the last 18 months. You can point the finger at the manager at Man United which I do, because I think Ole Gunnar Solskjaer was laughable in his management of those players.
"He brought a culture in which was like a Butlins holiday camp where the club was doing them a favour allowing them to play and not the other way around.
"Coming back from the European Championships and deciding he wanted to go on holiday before having an operation. It gets so far up my nose I can't imagine it because he should've been back, having surgery and getting ready for Man United, not going on holiday and then coming back and having surgery.
"The bottom line is, he didn't turn up. For Man United, they can't win. There's no way on god's green Earth you give him a contract on the basis of last year's performance.
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"Now you're caught in a situation where the clock's running down, you're into 18 months left and you want to give him a contract and the box seat is occupied by him."
However Jordan also believes the winger needs to recognise he owes the club more than just his gratitude, too.
"There has to be a balancing act," he said. "If he's a Manchester United academy product and understands the opportunity that was given to him and some of the patronisation he's had over the last 18 months, he'll sign a new contract, get a new bumper pay rise and commit his future to Man United.
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"That's what he should be doing. Man United are back in ascendancy, they've got a coach now that seems to get the understanding of what it means to be Manchester United.
He added: "Rashford and this discussion should be put to bed as quickly as it possibly can. But it'll be a horse-trade over enormous amounts of money.
"Doesn't earn his money the last 18 months, earns his money for six months, get a huge pay rise. There's the perversity of football finances."
Man United next face Barcelona in the second leg of their Europa League last-16 tie, with the side's currently level at 2-2 heading into the clash at Old Trafford.
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And there's no doubt Rashford will want to get on the scoresheet in the reverse fixture, too.