The dynamic midfielder has endured a torrid run of injuries in recent months and is likely to leave the Gunners at the end of the season after six years in north London.
Cazorla, 33, hasn't featured since October 2016 but did return to first-team training last week with hope of regaining full fitness ahead of next season.
The Spaniard is not short of potential options should he indeed leave Arsenal in the summer and, according to AS, a return to Villarreal is most likely.
The club's president made a personal call to Cazorla urging him to consider returning to La Liga and the early signs look good.
Cazorla has made 129 appearances for the Gunners, scoring 25 times.