Rashford, 18, played his first Manchester United game in February and has scored eight goals in 17 matches.
Hodgson has until 31 May to name his final 23-man squad for Euro 2016, which starts in France on 10 June.
Rashford scored twice on his Red Devils debut in the Europa League against FC Midtjylland after being drafted into the starting XI following an injury to Anthony Martial."The amount of time we're going to have with him is very, very short," Hodgson, 68, said.He also found the net twice in a 3-2 win over Arsenal and became the youngest scorer in a Manchester derby in the Premier League era with his winner against City in March.
England beat Turkey 2-1 on Sunday and have two more friendly matches - against Australia and Portugal on 2 June - before their first Euro 2016 Group B match against Russia on 11 June.
Hodgson added: "There is no doubt I think I made the right decision putting him in this large group because the lad has enormous talent and you will know from my past record that I'm not afraid to give young players a chance. I don't dismiss them on the basis of their age.
"But you will also know full well that where he is playing we actually have a lot of competition for places and there isn't an awful lot of chance for him to stamp his authority on myself and the coaching staff, because there is such a short period of time."
My England starting XI
Who do you think should start at Euro 2016? Step into Roy Hodgson's shoes and pick your XI - and then share it with your friends using our brand new team selector.Arsenal midfielder Jack Wilshere played 66 minutes in the victory over Turkey, despite starting just once for Arsenal all season having suffered a broken leg in September.
"With Arsenal I've been playing out wide, which is not me," Wilshere, 24, said.
"I'm not a wide man, but Roy seems to have faith in me in the middle, so I'm happy with that. I like to play anywhere in the middle.
Meanwhile, Leicester striker Jamie Vardy ended the season with a Premier League winners' medal and scored 24 league goals in the club's remarkable campaign.
The 29-year-old scored the winner against Turkey, but will miss the match against Australia because he is getting married on Wednesday.
"It will be a very quiet night on Wednesday," Vardy said. "Obviously I hope all the guests have a good time but I will have a quiet one.
"I've not got a curfew but at the end of the day I'm a professional and understand what has to be done, so I will be making sure I get plenty of sleep ready to come back in."
