The Mexican striker has been linked with a move away from Manchester United.
Hernandez has been rumoured to be on his way out of Old Trafford this summer after spending much of last season on the bench under David Moyes.
Van Gaal, however, says the Mexican poacher will have the opportunity to impress and refused to say he would sell the striker.
"I have to see if he performs how I want.," the Dutchman told the Manchester United website. "Now I can only see what he has showed under the guidance of another coach.
"He will arrive this evening and I will meet him, we will train and after that he will perform in a match and then I can say something about that."
Hernandez's arrival in Los Angeles for the club's pre-season tour of the United States was announced by the club's Twitter account.
At 26, the striker will be craving regular first-team football, but starting every game may not be a possibility at United, with Robin van Persie, Wayne Rooney and Danny Welbeck all looking to play up front.
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The Mexican remains one of the league's premier poachers in front of goal, and showed flashes of his ability last season. He must bring more than just goals to the team, however, if he is to remain at Old Trafford next season.
Newcastle United and Inter Milan are among the teams said to be seeking his signature.