Martial signed a new five-year contract in January, but has one goal in the past two months, with Solskjaer warning him and other out-of-form United players there is “no hiding place" at the club.
"Most of them have really impressed in their attitude and some need to get a reality check of where they're at," said Solskjaer.
“But most of these know they can improve if they keep working as they do.
“I've spoken to individuals and they know. Anthony is one I've spoken to, about what we expect from them.
“Anthony's got a massive talent, he's got a new contract and knows we believe in him, so he just has to keep working.
"I think anyone that plays for Manchester United has to deliver to stay in the squad and stay in the team
“Anthony is no different to Rashy [Marcus Rashford] or Rom [Lukaku] or Alexis or the many forwards we have to choose form.
“That's the great thing about - now it's down to the players and the ownership they take.
“Every day in training, every game when you're playing, there's no hiding place and everyone can see where your levels at."