Due to the financial implications of the coronavirus pandemic, it has been suggested that Spurs may prioritise free transfers during the next window.
However, given their need to sign a new right-back, manager Jose Mourinho may seemingly be provided with funds to bring in a player of his choosing.
According to Le 10 Sport, the Premier League outfit will explore the possibility of signing Castagne, who has fallen down the pecking order at Atalanta.
With just over a year remaining on his contract, the Belgium international is expected to leave the Italian side later in 2020.
The 24-year-old has spent the last three seasons at Atalanta, making 79 appearances in all competitions.