Apperibay travelled to London earlier this week to negotiate a deal with Arsenal, who still own 50 per cent of Vela's rights and can activate a buy-out clause included in his sale to the Basque club in 2012.
Although Apperibay has admitted that Arsenal are keen to activate the clause, he revealed at a dinner with reporters that the Mexican striker, who scored 16 goals last term, does not want to move back to the Gunners.
"We are fortunate that the player is keen to stay in San Sebastian with us and that's an important factor for Real Sociedad," said Apperibay.
The president also explained that the two clubs were yet to reach an agreement for the player, who Arsenal signed back in 2005 from boyhood club Guadalajara.
Apperibay was less optimistic about holding onto goalkeeper Claudio Bravo, and admitted the club were in "advanced" negotiations with Barcelona for the Chile international.
The Catalans have already signed German Andre Ter Stergen to replace the outgoing Victor Valdes, but need to bring in another goalkeeper as Jose Manuel Pinto is also departing the Nou Camp this summer.
Apperibay said the two clubs only had to "iron out a few details" before the transfer was finalised, and admitted he hopes the deal will include the loan of Barcelona midfielder Jonathan Dos Santos, who La Real tried to sign last summer.