Vela joined the Basque club for £4m last summer, but the Gunners have a buy-back clause that allows them to re-sign the starlet for a similar fee.
The 24-year-old has insisted that he wants to stay in Spain and hopes to sort out a long-term future with Sociedad in the summer.
He told Marca: "I know that Arsenal can pay £3.5m to sign me, but if Real Sociedad and I are good together, we can work something out.
"We will have to arrange something so I can stay here. I believe that we can do something so we can continue together."
Vela scored 13 times in 68 appearances during three seasons in England, which also included a short loan spell with West Bromwich Albion.