Rashford, 21, faces his biggest season yet after the sale of Romelu Lukaku to Inter Milan confirmed his position as United’s number one striker.
“For me it’s just about becoming the guy that’s responsible and reliable,” the England international said to the United Review ahead of United’s Premier League opener at home against Chelsea on Sunday.
“I feel like that’s the next step for me. Everything goes in order of the way it should be done.
“I remember these similar steps when I first went into the under-18s and it takes you a season to grow into that standard of football.
“Before you know it, you’re one of the leaders there and you take responsibility on the pitch. Now I’m in that situation for the first team.”
Rashford, who joined United at the age of seven, signed a new four-year contract in July to keep him at United until 2023.
“I give my life for the club and that’s the most important thing,” said the forward, who has scored 45 goals for the club in 170 appearances.
“For me, when you’re in a squad with a lot of young players who share the same ambition and have the same drive, I can only see us succeeding.
“It might take us some time, but if we all stick to the game-plan, work collectively as a team, and we’ve got a good manager who knows the club and who shares the same ambition, who knows what we can achieve?”
Rashford scored 13 goals last season as Solskjaer succeeded Jose Mourinho in December.
The Norwegian, himself a former United striker, has put his faith in Rashford to help the Red Devils improve on last season’s disappointing sixth-placed Premier League finish.
“It’s about putting those experiences together now,” said Rashford.
“That’s how you know the way forward. Right now I feel like mentally and physically I’m more prepared to do it than in the past, especially physically.”
