The Sun says the England striker has just two-years left on his £70,000-a-week contract, with the option of a another 12 months.
Old Trafford chiefs want to tie the 20-year-old down on fresh terms, to reward him after coming through the United academy.
A club source said: “Marcus loves it here but there are concerns with what the boss could do this summer.
“Everyone is currently on the same page.
"This is his club, but you never know what is going to happen.
“United just have a nagging feeling that if they leave it much later into his present deal, they won't hold all the cards.
“He is still struggling to make the starting eleven under Jose, so it is likely."