The England international, who is not at this year’s World Cup, announced he is to leave Arsenal this summer on a free transfer after not being guaranteed time on the pitch under new manager Unai Emery.
Wilshere played 38 times for Arsenal in all competitions last season, suggesting his injury worries are in the past. In those games, he scored twice and assisted six times.
In addition to Saints, the likes of West Ham United, Wolverhampton Wanderers, Sampdoria and AC Milan have all been linked with Wilshere’s signature.
In Wilshere’s statement confirming his departure from Arsenal this summer, he said: ”I felt that I was ultimately left with little choice but to make the decision that I have due to purely footballing reasons.
”Such was my desire to stay that I had in fact recently agreed to sign a financially reduced contract in order to commit my future to the club.
”My intention throughout these discussions has always been to remain an Arsenal player. I have been on the books at Arsenal for 17 years and have always felt part of the fabric of the club.
”Following my meeting with the new manager I was made aware that although the reduced contract offer remained, it was made clear to me that my playing time would be significantly reduced should I decide to stay.
”I am sure everyone can understand that at this point in my life and career I need to be playing first-team football and following my meeting with Mr Emery I came away feeling that it would be very difficult for me to do so at Arsenal.
”Given this, I feel I have no option but to pursue other opportunities in order to progress my career on the pitch.”