He was loaned out to Celta Vigo, Salamanca and Osasuna earlier in his career to aid his development and to help get him his work permit.
Last term, he was again farmed out, but this time it was in England to Premier League outfit West Bromwich Albion.
Vela's agent, Eduardo Hernandez, said: "I'm going to fly to London to finalise things with Arsenal.
"We have three teams in Spain that have made offers and we think that playing in Spain would be a good move for Carlos.
"Arsenal are happy for him to go out on loan and we hope to find a solution by next week."