The Manchester United striker, 18, scored twice on his debut against FC Midtjylland and then two more in the win over Arsenal on Sunday.

Rashford, who did not score against Watford on Wednesday, has only been capped at under-18 level for England.

"I would neither rule him in or rule him out, I just hope he can do well," Hodgson said.

"I have been watching Rashford for two years, so I have known about him for a long time. He is in our system."

He added he was delighted that an England Under-18 player was getting chances in Manchester United's first team.

"Most of all, 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.

"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 came into Louis van Gaal's side with fellow strikers Wayne Rooney and Anthony Martial injured but looks set to remain a part of the first-team picture at Old Trafford for the remainder of the season.

Meanwhile, Hodgson says Jack Wilshere could find his way into England's Euro 2016 squad despite the fact he has yet to play for Arsenal this season.

The 24-year-old midfielder has been sidelined since breaking his fibula on the eve of the current campaign, the latest in a long list of injury problems.

Hodgson has two friendly internationals - against Germany and Netherlands - this month before he must name his squad for the finals in France.

Those two matches are likely to come too soon for Wilshere, who is expected by his Arsenal manager Arsene Wenger to be fit in the next three to four weeks.

But Hodgson said a lack of game time does not mean he would not call up the 28-cap player.

"Players are either fit to play or not," Hodgson said. "Whether they play 30 games, 40 games, 10 games, 15 games, eight games, I don't understand that.

"For me, it's all about the class of the player. It's about who is in form and out of form. Even to some extent I have to rely on others' judgement on that.

"Form is transient, but class isn't, " he added. "We need classy players and players we can trust and players we know what they will give us and players who have the desire, motivation and wish to play for England, to do all that's necessary.

"Luckily we have some of those. But let's be realistic, we are not in the 60, 70 and 80s when it comes to those. If there are 30 players who reach the high standards I demand, we will have to pick 23 from them."

(BBC)