Manchester United forward Rashford, 18, has seven goals in 13 outings since making his senior debut in February.
Hodgson has been "very impressed" with the teenager but said it was "unlikely" he would take him to France.
"I think it would be a very bold decision to put him in," added Hodgson.
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Rashford, who is still six months short of his 19th birthday, marked his senior debut with two goals against FC Midtjylland in the Europa League.
Since then, the England Under-20 international has scored four Premier League goals, including winners against Manchester City and Aston Villa.
The youngster also scored at West Ham to help United book an FA Cup semi-final date at Wembley with Everton.
In March, Hodgson said he would "neither rule him in or rule him out" when asked if Rashford could make his squad for France this summer.
Hodgson has numerous attacking options in the shape of United's Wayne Rooney, Tottenham's Harry Kane, Leicester's Jamie Vardy, Liverpool's Daniel Sturridge and Arsenal's Danny Welbeck.
In addition, West Ham's Andy Carroll has staked a claim after scoring six goals in his last five league games.
"I think it would mean possibly leaving someone behind who, at the moment, has more reason to be called up," said Hodgson when again asked about Rashford.
"But you never know. The fact is it would be foolish as well to say 'no, no, he's not ready, he can't do it'.
"I am sure he could do it.
"It's not inconceivable but it looks unlikely to me with the current players we've got and the competition for places in that area of the field."
England boss Roy Hodgson says he would have to sacrifice a player who has "more reason to be called up" in order to fit teenage striker Marcus Rashford in his Euro 2016 squad.