Wilshere, whose current Gunners contract expires next summer, spent last season on loan at Bournemouth after being deemed surplus to requirements by head coach Arsene Wenger.
The 25-year-old missed the end of last season with a broken leg, but has since returned to fitness for the Under-23 team.
It is understood that the midfielder's Arsenal career is over, however, and a number of clubs have been linked with a move for the England international before the end of the month.
According to Estadio Deportivo, La Liga side Betis have been offered the chance to sign Wilshere before the close of the summer transfer window, and the midfielder is said to be considering the move.
Wilshere, who came through the youth system at Arsenal, missed out on a spot in the latest England squad.