The 25-year-old, who joined United in 2010, is still trying to establish himself under David Moyes after starting just two games this season.
He did score the winner against Liverpool in the Capital One Cup last month, but has been eased back into the United fold by Moyes after playing for Mexico in the Confederations Cup in the summer.
Hernandez enjoyed the reputation of an impact player under Moyes' predecessor Sir Alex Ferguson, but he remains determined to secure a starting role with the Premier League champions.
"I strive for that [to start more games]," Hernandez told Mexican TV station Deportes Telemundo.
"I am working towards that - earning a spot as a starter. I know that my performance on the pitch will allow me to achieve that goal someday either here [in Manchester] or elsewhere for any other club.
"I am going on four years here [at Manchester United] and really, like I have always said, I am happy to be able to play for one of the best clubs in the world, doing my best every single day to earn more minutes on the pitch.
"I just need to be given more opportunities to showcase what I can do, because all of us want to be able to contribute our part so this team can win championships."
Hernandez also has no issues in competing with the likes of Wayne Rooney, Robin van Persie and Danny Welbeck for a spot up front.
He added: "What better way to compete anywhere in the world than to compete with them?
"The competition inside the team has always been really healthy and I think that helps the team a lot, because there are so many quality players that every one of them wants to earn a starting spot.
"The practices and matches coming up will force us to step up and help the team grow both at an individual and collective level."