The 25-year-old Mexican joined La Liga side Real Sociedad in 2012 for a reported fee of £4million, following a successful loan spell at the Basque side.
Since his permanent switch to Spain, Vela has racked up 30 goals in all competitions and has reportedly attracted interested from the Gunners - who may look to activate their buy-back clause on the forward.
Following a disappointing first spell at Arsenal, who he joined as a teenager in 2008, Vela admits he would not repeat his errors if he did move back to north London.
"If I have to return, I will do things in a different way," he said.
"What happened in the past will not be repeated."
The Mexican, who won't feature in this summer's World Cup due to an ongoing dispute with his country's football association, is hoping to negotiate a deal that will suit all parties.
"We will try and reach an agreement in which we all win - Real, Arsenal and me. We must see what can be done," he said.
"We will decide what will be my future, it is all about finding the best way to be happy."