Spurs have tracked Maddison, 26, for several seasons, and new manager Ange Postecoglou is thought to be keen on the move. Sources told ESPN that negotiations are ongoing, with the two sides are still trying to find mutual ground on the transfer fee.
Maddison and his Leicester teammates were relegated from the Premier League last season, during which the midfielder registered 10 goals and nine assists from 30 league appearances.
He was a member of England's World Cup squad last year but arrived in Qatar with a knee problem and did not feature at the tournament. He has since expressed a desire to remain playing top-flight football with Euro 2024 coming up next summer.
Maddison joined Leicester in 2018. He previously enjoyed spells at Coventry City, Norwich City and Aberdeen.