The England international is out of contract at the end of the current campaign, with talks over a new deal at the Emirates having hit the buffers.
Wolves scured promotion to the Premier League at the weekend and are now hoping to complete an audacious move for the playmaker.
As things stand, Wilshere will leave Arsenal in the summer, with the 26-year-old reluctant to accept the pay-cut offered by Arsenal.
Wolves have shown their ambition in the transfer market with regularity in the last year of so, luring the likes of Helder Costa, Diogo Jota and Ruben Neves to the club, despite being in the Championship at the time.
Following Neves' impressive performances in the engine room this season, the Midlanders are keen to find the Portuguese a partner in the middle of midfield, with Wilshere considered the ideal man for the job.