Betis were strongly linked with a move for Wilshere during the summer, but the 25-year-old decided to stay at the Emirates Stadium to fight for his place.
Wilshere is yet to begin talks over a fresh deal with the Gunners, however, and his current contract will expire at the end of the season.
The midfielder has not started a single Premier League game this term, and was overlooked by Gareth Southgate for the latest England squad despite a number of withdrawals.
According to The Sun, Betis 'believe they are close' to securing a deal for Wilshere, who could sign a pre-contract with the La Liga club in January before moving on a free transfer next summer.
Betis are currently eighth in La Liga - just six points off the top four - after making a solid start to the season.