Terriers chairman Dean Hoyle has seen the Leicester City man score three goals in six appearances since crossing from the Foxes and he is hoping to extend the deal which expires on January 1 so they have a quality target man following Jordan Rhodes' move to Blackburn Rovers.
"I think Jermaine's view is he'd probably like to stay with us for the season and hopefully that can be arranged," Hoyle told BBC Radio Leeds.
"He loves it here and gets on very well with Simon Grayson.
"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.