The Spain international has been on the fringes of the first-team this year and could depart the club in the summer.
The 31-year-old central midfielder made 233 appearances for the Liga side during two spells with the club.
Cazorla spent the early years of his career at El Madrigal before returning the club after a one year spell away at Recreativo Huelva.
After helping secure UEFA Champions League football for Malaga with a fourth place finish in 2012 - ending the season as second top scorer - Cazorla made a £10 million switch to north London to join the Gunners.
The Spanish player has been limited to just 20 appearances this term in a campaign stricken with injuries. However, he is expected to make a return this weekend and feature for Arsenal in their clash with Norwich City on Saturday.
According to a report in the Daily Mail, Cazorla has been impressed with Villarreal’s run to the semi-finals of the UEFA Europa League.
As quoted in AS, the playmaker said he would be open to returning to his former club.
"I do not rule out returning to Villarreal one day,” he said. “Everybody in the world knows that Villarreal are a very special club to me."