Manager Ole Gunnar Solskjaer said Greenwood would be in contention for starting spot in the Premier League opener against Chelsea, after then 17-year-old scored the opening goal within seven minutes against Leeds.
Speaking about Greenwood, Rashford said: "You have to understand people's characteristics. He's quite a laid-back person, so I don't think it does him any good to put things in his head constantly.
"But his natural abilities are frightening and the manager is doing a good job guiding him in the right direction. The more he does that the more his talent will come through."