The former Arsenal star has been strongly linked with a move to Ibrox following his release from West Ham United.
Wilshere has been showcasing his ability and fitness in exercise drills posted on social media, making clubs aware he is ready for a move.
The 28-year-old hasn’t hit the levels expected of him. Injuries stunted his development and he played just 18 times for West Ham across two seasons.
Earlier this month PA reported he would be keen on a move north.
A source said: "Rangers would be an option for Jack if there had been any contact. So far, however, there hasn't been any.
"Jack thinks Rangers are a great club.
"They tried to take him on loan when Walter Smith was in charge back in 2010 just as he was starting out at Arsenal but he ended up going to Bolton."