Spurs are holding out for ?6.5million but Sevilla's offer is currently well short of that price.
The Mexican international scored in his country's 4-2 Gold Cup final triumph over the US on Saturday and is highly regarded in Spain.
Highly regarded: Giovani Dos Santos celebrates scoring in the Gold Cup final
But Dos Santos has only made nine starts in three years at White Hart Lane since joining for an initial ?4.7m from Barcelona in 2008.
The 22-year-old, who was hailed as the new Ronaldinho while at Barca, has been farmed out on loan to Ipswich, Galatasaray and, most recently, Spanish side Racing Santander.
Flop: Dos Santos has only made nine starts in three years for Spurs
Spurs boss Harry Redknapp needs to sell players to raise money for new signings and has made it clear that Dos Santos - who was signed by his predecessor Juande Ramos - is not part of his plans.
The attacking midfielder is keen to rebuild his career in Spain after a successful spell at Racing and all that is left to do is agree a fee.
But with Barcelona set to collect 10 per cent of any transfer fee, Spurs are driving a hard bargain.
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?Explore more:People: Giovani Dos Santos, Juande Ramos, Harry Redknapp Places: Barcelona, Spain
Source: Daily Mail
Source: Daily Mail