Spurs are believed to be keen to acquire another defender before the deadline, and a recent report claimed that Duarte had been identified as a target for Nuno Espirito Santo's side.
However, according to Onda Vasca, Tottenham's first offer was considered 'derisory', and the North London club will have to 'add a lot' to their previous bid to convince Granada to sell.
The 26-year-old has played the full 90 minutes in both of his side's La Liga matches this season, while he has featured on 83 occasions for the club in total since arriving from Sporting Lisbon in 2019.
Duarte - capped on two occasions by the Portuguese national team - has less than two years left to run on his contract at Nuevo Estadio de Los Carmenes.
Tottenham are also allegedly facing the prospect of missing out on a deal for Wolverhampton Wanderers attacker Adama Traore.