The 20-year-old, who has two years left on his current United deal, suffered an inconsistent run in the team last season, starting 17 Premier League games but appearing 18 times from the bench.
According to The Sun, however, the England international is keen on extending his stay at Old Trafford, and talks could see his wage rise by £50,000 to around £130,000 per week.
"The club want to sit down after the World Cup, even if his camp want to see what Jose does in the market. The club want to hike his money up once some of the higher earners are out of the door in the next few weeks," a source told the newspaper.
"Rash wants to be put at ease and the club want to show him how highly they value him and that he has a long future here."
Rashford, who joined United aged seven, has also been linked with loan moves to Newcastle United and Leicester City.