Rashford and Shaw are considered part of a key group of core players that United want to keep at Old Trafford and they are keen to push ahead with negotiations despite uncertainty over the identity of the club's next permanent manager.
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Fernandes has verbally agreed terms on a new five-year contract with an announcement expected after the international break.
Sources at Old Trafford have stressed the fresh deal is designed to bring the midfielder in line with the highest earners and reflect his contribution since arriving from Sporting Lisbon in January 2020 rather than as reward for a season during which the 27-year-old has suffered a dip in form.
Fernandes scored 28 goals in all competitions last season but has managed just nine so far this term.
Rashford and Shaw have deals until 2023 with the option of an additional year and United are keen to tie them down to long-term contracts.
Erik ten Hag, Mauricio Pochettino, Luis Enrique and Julen Lopetegui are among the contenders to take over as manager with the club hopeful of making an announcement before the end of the season to allow the new man to have influence over the summer's recruitment plans.
But sources have told ESPN that, like Fernandes, Rashford and Shaw are considered important members of the squad with the decision to extend their contracts without the explicit consent of the next boss.
Sources have told ESPN that Rashford is open-minded about his future and is in no rush to decide his next move.
The 24-year-old has struggled this season and lost his place in the England squad for friendlies against Switzerland and Ivory Coast this month.
Rashford is keen to win back his place at United and earn a spot in Gareth Southgate's squad for the World Cup, which is due to start in Qatar in November.