The Gunners have offered the England international a new deal which requires him to accept a pay-cut. He is keen to continue with the Gunners, but his contract stand-off has alerted other clubs.
The report claims that the Merseyside club are very keen to sign him and could offer him a better deal than what he is being offered.
Wilshere is reportedly on £90k-per-week wages, which can rise to £120,000 per week if lucrative bonuses are taken into account.
Should Newcastle United be interested and join Everton in the race for Wilshere?
The Magpies were one of the many clubs that had shown interest in the 26-year-old last summer. The Telegraph reported in July that the Magpies were weighing up a move for the Arsenal midfielder.
Wilshere seems to have shaken off his injury-prone image and has been playing some of his best football in the last couple of years.
In fact, he is one of the consistent performers for the Arsenal side that look out of form at the moment. He would be available on a free transfer this summer, and Newcastle would be making a huge mistake not to rekindle their interest.
Central midfield is one area where Rafael Benitez could look to bring a top player to play alongside Jonjo and Wilshere could fit the bill nicely.