Thrust into the spotlight by Louis van Gaal before becoming a regular for Jose Mourinho, the 21-year-old is now flourishing under the guidance of caretaker manager Ole Gunnar Solskjaer.
Rashford netted his 10th goal of the season in the 1-0 win at Leicester on Sunday, when the forward became the second youngest player to reach 100 Premier League appearances for United after Ryan Giggs.
The Welshman spent his entire playing career at Old Trafford and it is thought that the club are looking to tie academy graduate Rashford down to an extended deal.
The England striker’s contract expires next year and, while United have the option to extend it until 2021, negotiations have begun over a fresh agreement.
The club are also working on a new contract for goalkeeper David De Gea, having last week tied forward Anthony Martial down until at least 2024.
But midfielders Juan Mata and Ander Herrera have also to agree new deals to stay beyong the end of this season.
Asked about Rashford and Martial pushing each other on, United caretaker boss Solskjaer said: “Yeah, through healthy competition but they can also create a relationship.
“Hopefully they will play many, many years together.
“So, if they get an understanding of each other because both are very good at coming in off the left, but if one of them plays central then the other one has to do opposite movements.
“In the coming years we’ll see loads of combinations between those two.”