Real Sociedad have insisted there is "nothing concrete" regarding an offer for Antoine Griezmann after the club president held discussions with Arsenal.
Club chief Jokin Aperribay travelled to London this week to hold talks with the Gunners over the future of Carlos Vela.
After offloading the Mexican striker to Real Sociedad in 2012, the Premier League side inserted a buyback clause into his contract to give them the option of resigning their former player for a fraction of his current market value.
Although Aperribay did confirm that Arsenal informed him of their intention to activate Vela's buyback clause, he returned to San Sebastian with no developments regarding Griezmann's future.
"I will no comment on whether we have received an offer for Griezmman or not because it's commenting on hypothesis," Aperribay told Spanish radio station Cadena Ser.
"If an offer arrives we will talk about it, but at the moment there is nothing concrete."
Griezmann, who is part of the France squad that gets their World Cup campaign underway against Honduras on Sunday, has been heavily linked with a move to the Gunners, Manchester United and Paris Saint Germain after a sparkling campaign in La Liga.
The attacking midfielder struck 16 goals and provided three assists alongside Vela in Real's fearsome attack en route to earning a place in Didier Deschamps' French squad.
Although he remains highly valued by La Royal, reports in the Spanish press have suggested the club may be willing to sell Griezmann to Arsenal for less than his £25m release clause, if the Gunners waive their right to resign Vela.
Vela struck 16 league goals for his club last season where he solidified his reputation as one of La Liga's most potent attacking outlets and caught the attention of champions Atletico Madrid, who have reportedly identified him as the man capable of filling to void soon to be left by the Chelsea-bound Diego Costa.
But while reports in Spain suggest Vela's burgeoning reputation could now command a fee of up to £25m, Arsenal have informed Real Sociedad of their plans to bring the striker back to north London for just £3.2m.
"Arsenal have informed us that Vela would be with them next season," Aperribay said on Tuesday.
Real were reportedly told by Arsenal last month that it would cost them €12m to buy Vela outright and eliminate Arsenal's clause, but Aperribay refused to shed any light on the ongoing negotiations.
"There are no discussions in this regard and therefore it is difficult to talk about whether we would be near or far, we will see in the near future if we go a little and accomplish something for Real."