Hodgson has been keeping a close eye on the 18-year-old forward, who scored twice on his debut against FC Midtjylland in the Europa League and got two more in Sunday's Premier League win over Arsenal.
"I would neither rule him in nor rule him out, I just hope he can do well," Hodgson was quoted by British media as saying at a Euro 2016 coaches' briefing in France on Thursday.
"I have been watching Rashford for two years, so I have known about him for a long time. He is in our system."
Hodgson added that while he was pleased to see an England Under-18 player featuring in United's first team, he hoped Rashford would not have too many expectations placed on him.
"My hope for Rashford, and it is a vain hope, is that he will be allowed to develop in peace and it won’t suddenly be a question of, 'You have scored two goals for Man United and you’re going to be the next Cristiano Ronaldo' or every time he has two or three bad games he is a flash in the pan.
"Let’s hope the lad gets a chance to develop in the same way as Raheem Sterling, Ross Barkley, Wayne Rooney, David Beckham and Paul Scholes," Hodgson added.
"Scoring four goals in three games is a great achievement and if he can keep that up, it is great for Manchester United and England."
Rashford was a late inclusion in United's team against Midtjylland after Anthony Martial was injured in the warm-up and struck twice in a 5-1 win in the last 32, second-leg clash.
(Writing by Ken Ferris; Editing by Peter Rutherford)
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