Wilshere is currently still recovering from the fractured leg he sustained towards the end of last season, but he is still attracting plenty of interest from within the Premier League and around Europe.
Both West Ham United and Sampdoria have allegedly identified the England international - who has just 12 months left on his contract at the Emirates Stadium - as a potential signing before the end of August.
However, according to The Telegraph, Swansea head coach Paul Clement is currently considering whether to make an approach for the 25-year-old as he looks to strengthen in midfield.
Jack Cork has left for Burnley, leaving space in the middle of the park, and Swansea would be able to offer him first-team football after his productive spell with Bournemouth last season.
Wilshere's asking price could prove to be a stumbling block, however, with Arsenal currently demanding around £20m for a player who has come through their youth system and made 159 appearances in all competitions.