The 18-year-old striker shot to prominence in the last week with four goals in three starts under Louis van Gaal and is now in the frame for a senior international call-up.
Having previously featured for the England Under-16 and Under-18 sides, Three Lions boss Hodgson claims he could now be willing to hand Rashford his first cap, but is wary of expecting too much.
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“I hope he is allowed to develop as an 18-year-old should and people don’t try to put him under enormous pressure," he said at a Uefa international coaches workshop.
"I would neither rule him in or rule him out. I just hope he can do well.”
Rashford is reportedly in line for a new contract at Old Trafford following the past week's impressive exploits, and the England boss is glad to see him shine, having been convinced of his ability for some time.
He added: “I have been watching Rashford for two years, so I have known about him for a long time. He is in our system.
"That is wonderful and long may it continue. I hope he has a good end to the season.
“He plays for the Under-18 team, so we are delighted that a player playing for our Under-18s, players who we believe in and who we think have got a bright future, are getting chances in the first team at club level.
“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.
“Let’s hope the lad, at 18 years of age, gets a chance to develop in the same way as Raheem Sterling, Ross Barkley, Wayne Rooney, David Beckham, Paul Scholes... you can name as many as you like."