Spurs are hunting for bargains in the transfer market and want to sign many young players in the coming years, and Kelman is one of those targets.
The Daily Mail claims the club are looking to sign the 18-year-old this summer, while they also attempted a deadline day move for the player in January.
Southend are in League One and appear set for relegation.
When the club officially go down, Spurs may come in with an offer they cannot financially refuse.
The COVID-19 pandemic means that lower league clubs cannot turn down offers, even six figure ones, from top teams.