Wilshere, 29, will reportedly sign a six-month deal with the Cherries.
He has been training with the Cherries for the past three weeks after being left without a club following his exit from West Ham in October.
Bournemouth manager Jason Tindall previously admitted he was considering offering the ex-England midfielder a contract.
Tindall said: “Jack is still training with us. It is good to have him and he is looking sharp in training.
“We will keep monitoring that situation in the next week or two.
"We'll see where Jack is at and what we feel as a club would be the best thing moving forward."