The 26-year-old's contract is set to expire in the summer, and despite recent praise from Arsene Wenger, he has yet to be offered a new deal.
Taking to Instagram on New Year's Eve Wilshere reflected on a challenging 2017, and looked ahead to what he hopes will be a successful 2018.
Alongside a picture of himself at Bournemouth, the midfielder wrote: "So this time about a year ago, I was a Bournemouth player sitting in the stands at the Vitality watching AFCB v AFC wondering if I would ever play for Arsenal in the Premier League ever again.
"After another set back, I never stopped dreaming and believing. If 2017 has taught me anything it would be NEVER GIVE UP!!! Love playing for this club and long may it continue. Looking forward to 2018."