The 25-year-old, who is the club's top scorer with eight goals this season, is set to become a free agent when his contract expires next summer.
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It is expected that the Red Devils will, at the very least, trigger a one-year extension in his clause to keep him at the club until 2024.
Ahead of the World Cup final which saw Argentina beat France, it was reported how Rashford was set to become United's highest-paid player of all time.
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The Daily Star claimed United were set to offer the England international the whopping salary to fend off interest from Paris Saint-Germain.
As it stands, Rashford is free to talk to PSG - and other European clubs - in January over a free transfer next summer.
A United fan account on Twitter shared the transfer talk from the Star, which saw Rashford immediately shut down the news.
Rashford insisted that his only focus is on helping United secure a top four finish, and not about his future.
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He tweeted: "Can we please stop making up these stories?
"Mines [sic] and the club's objectives are to hopefully get into the Champions League this season.
"This isn't helpful. Thank you."
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As well as his impressive form for United this campaign, he was also England's joint-top scorer at the World Cup with three goals.
His displays in Qatar led PSG president Nasser Al-Khelaifi to state his interest in securing Rashford's services.
He told Sky Sports: "He's another player that is really amazing. And for free? To have Rashford for free, every club would run after him, definitely.
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"We're not hiding it, we spoke before and (there was) interest, but the moment was not a good moment for both sides. Maybe, summer, why not?
"Today if he's a free agent of course we can talk to him directly, but we are not going to talk to him now.
"Let him focus on the World Cup. Then after in January, hopefully, if we're interested we will talk to him."
United boss Erik ten Hag recently compared Rashford to Les Parisiens forward Kylian Mbappe as he praised the Three Lions man for making huge improvements this term.
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