Hernandez has been ill for the past fortnight, while Wilshere’s troublesome ankle has been playing up again.
Hernandez still has a chance of featuring at the weekend, but Wilshere doesn’t according to Pellegrini.
"We have nothing special other than Hernandez is sick and has had a virus for the last ten days, so he's at home,” he said.
“Jack injured his ankle two days ago, so we'll see how he is on Tuesday after he has had a medical review. He is not going to feature on Sunday.”
Wilshere’s absence for West Ham could cause Pellegrini a selection dilemma in midfield.
Wilshere has been a regular starter for the Hammers, but it could be that Mark Noble is paired with Carlos Sanchez at the weekend.
Hernandez’s best chances of featuring for the Hammers may come as a substitute.
Hernandez, meanwhile, has been struggling to break into the West Ham side ahead of Marko Arnautovic so far this season.