The 46-year-old returns to White Hart Lane on Wednesday for the first time as a player or manager since spending 10 years at the North London club between 1990 and 2000.
"I have ambitions and I want to manage in the Premier League. If I could pick a club, Spurs would be my dream job," Edinburgh is quoted by Sky Sports News as saying.
"But then do you ever get your dream job? Some people do. I started in the seventh tier of English football and I'm now two away. I'm a lot closer than I was.
"That's my dream. Winning at White Hart Lane would help of course. You get recognised by your team doing well and getting good results, and hopefully that's the case come Wednesday."
Gillingham have already knocked out Premier League side Watford away from home in the League Cup this season.