Spurs have tracked the 26-year-old for several seasons and the club's new head coach Ange Postecoglou is thought to support a summer move.
Leicester are willing to let Maddison leave after their relegation from the Premier League with the midfielder wanting to continue his career in England's top flight as he seeks to push for a place in the national team squad for Euro 2024.
Reports suggest Leicester could demand more than £50 million for Maddison, who has just one year remaining on his contract.
Spurs are likely to face competition from Newcastle United for his signature. Arsenal were also previously linked with a move, although the north London club are prioritising a move for West Ham United's Declan Rice while also retaining an interest in Brighton & Hove Albion midfielder Moises Caicedo.
Maddison registered 10 goals and nine assists from 30 league appearances last season. He was a member of England's World Cup squad last year but arrived in Qatar carrying a knee problem and did not play a single minute in the tournament.