The 28-year-old joined from Leicester City in September and has since scored three goals in six games.
He is due to return to Leicester in January, but Hoyle has praised the contribution of the former Everton striker.
"I think Jermaine's view is he'd probably like to stay with us for the season and hopefully that can be arranged. He loves it here and gets on very well with Simon Grayson," he told BBC Sport.
"Jermaine is a fantastic character. Before I met him I thought he had a bit of an attitude, but since I met him he's been a cracking guy. We'd like him to be around longer term, but ultimately it's Leicester's call."
Huddersfield currently occupy sixth spot in the Championship table.