Dos Santos has failed to become a regular at White Hart Lane, following his £5million move from Barcelona last summer.
But Dos Santos, who is one of Mexico’s biggest stars, is desperate for a move away from Spurs in order to save his World Cup hopes.
Deportivo coach Miguel Angel Lotina said: “Giovani is the sort of player that the club needs at the moment. It is a complicated deal but we hope we can reach an agreement with Tottenham.”
The Daily Mirror reports that Spurs may consider allowing Dos Santos to join Deportivo in January with a view to a permanent move.
Deportivo is keen on bringing in Dos Santos on loan now if they can manage to get permission from the Spanish Football Federation and UEFA.