Rashford has two years left on his current deal, with Manchester United believed to be keen to keep him.
The young striker has flourished since Ole Gunnar Solskjaer has taken over as caretaker boss after struggling under Jose Mourinho.
Rashford’s recent record has seen him score eight goals in his last 15 matches ahead of a Premier League clash with Liverpool on Sunday.
He has started all but two of the 13 games under Solskjaer, with the likes of Anthony Martial and Phil Jones having also impressed with the Norwegian at the helm.
That has led that pair to extend their contracts at Old Trafford with Martial reportedly now earning £200,000 per week.
And the Mirror claim that United know it’s key to tie Rashford down to a new deal before fans ‘revolt’.
It’s believed that Manchester United executive vice-chairman Ed Woodward is confident of confirming a new deal for Rashford in the coming weeks.
It comes with Real Madrid believed to be interested in the forward as they still hunt for a replacement for Cristiano Ronaldo.
But with David de Gea also in ongoing talks with the club, Woodward is remaining positive over the future of the United players.
He said: “It’s pretty well known the end dates of the players’ contracts.
“We are a long way through the ones we had planned to do this season but obviously we want to finish off the final few as rapidly as we can.
“Possibly, by the time we get to the summer we will be in a much stronger position with regard to the average tenure of each contract with our key players.”
And Solskjaer, who is in place at the helm until the end of the season, believes talks are a good sign for the Red Devils.
“The club’s working on [contracts for] a few players, I don’t know how far but it’s a statement from the club we want to keep our best players,” Solskjaer recently said.