Bayern Munich forward Toni Kroos left the door open for a switch to the Barclays Premier League in the summer.
Tim Sherwood claims the "silence is deafening" from the Tottenham board amid speculation he could be replaced as manager.
The 18-year-old midfielder made his first-team debut as a 16-year-old at Derby in September 2011and made three further appearances in the Championship before struggling with a long-term hip problem that kept him sidelined last season.
"I'm obviously delighted and glad to be here for the next four years," Digby told the club's official website. "Hopefully we can progress as a club.
"Last week, I sat down with my agent and he said that the club wanted to keep me here for the next four years. We discussed various things and obviously I was thrilled.
"I just want to get back in the team and continue playing football.It's such a big deal for a young player.
"To know I'm wanted as part of the club's future plans gives me a massive boost."