The player has become an established member of Aidy Boothroyd's first team this season, making 10 appearances, but remains on a scholarship rather than pro deal at Sixfields.
The Cobblers boss has previously stated he intends to discuss a contract with Hornby, but wishes to keep him on youth terms for the moment to maintain his hunger.
Hornby, 17, whose father played for Burton and Yeovil, told the Northampton Chronicle: "You want to become a footballer, but I've just got to keep working hard and hopefully that will come.
"I've got no complaints. I'm in the side and I'm playing regularly so I have got nothing to complain about at the moment."