Ahead of Sunday's game against Bournemouth, Solskjaer was asked if he could have an impact on his front men just like he has done with midfielder Paul Pogba, who scored twice and made two assists in the last two games under the Norwegian.
"I don't agree I've done that with Paul and I can do that with Romelu and Alexis. It's up to them when they get a chance," Solskjaer told a news conference.
"That's the name of the game when you're a footballer. You've got to do it yourself. Yes, you want help from your manager and your team mates.
"I'm here to help them, guide them on the path, and then it's up to them to do it on the pitch."
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Pogba struggled to influence games under former boss Jose Mourinho this season amid a reported rift between the pair but the France World Cup winner has played with more freedom under Solskjaer who has backed his team to express themselves.
"I give them guidelines. There's been loads of talk about freedom of expression, but that's how I've always been as a manager. You can't tell all the players what to do," the Norwegian added.
"They're here for a reason -- they're good players. It's up to them to use their imagination, creativity and enjoy playing for this club, because that's the best time of your life."
Lukaku, Sanchez and Anthony Martial all trained on Thursday after missing Wednesday's 3-1 league win over Huddersfield Town, while defender Chris Smalling is likely to be out until the game at Tottenham Hotspur on Jan. 13.
United are sixth in the table with 32 points from 19 games.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
