Wilshere is out of contract at the end of the season and has rejected a new deal with the Gunners. The midfielder is unhappy that the club's offer includes close to a £20,000-per-week pay cut, according to Football.London's Charles Watts.
Everton would be willing to match his current wages as well as offer him "a sizeable signing-on fee," per Watts.
The 26-year-old has endured an injury-plagued career, but he has proved his fitness at Arsenal this season by making 35 appearances in all competitions.
However, he has not managed to consistently impress, which has left question marks over his ability at the highest level. Freelance writer Huw Davies summed up the situation neatly:
Manager Arsene Wenger has said he wants Wilshere to stay and hopes the midfielder will agree to the proposal on offer, per BBC Sport.
However, Wilshere has said Wenger was happy for him to leave last summer, as Henry Winter at The Times highlighted in March:
Arsenal's reluctance to offer Wilshere a big-money contract is understandable given his injury record. However, they will lose him on a free transfer in the summer if he does not renew.
Former Arsenal defender Martin Keown believes it would be a disaster if Wilshere leaves, per Indy Football:
A move to Everton would also see Wilshere reunited with former Gunners team-mate Theo Walcott, who moved to Goodison Park from Arsenal in January 2017.
There's no doubt that a fit Wilshere is a quality midfielder who has yet to realise his potential. However, his injury record is a concern and is likely to have an impact on any decisions regarding his future.