"I've always said, 'We love Jack, we would love to sign him'," Howe, whose Bournemouth side were held to a goalless draw by Southampton on Saturday, told British media.
"But that decision will rest with Arsenal, with Jack, with other people: it's out of our hands. And Jack may well see his future elsewhere."
With midfielder Andrew Surman suffering a knee injury at Southampton, Wilshere, Harry Arter and Jordon Ibe are in contention to replace the South African in the starting lineup for the league match at Liverpool on Wednesday.
"We've got real competition in that position," Howe added.
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"You've seen Harry Arter come off the bench: he's been outstanding for us this season. You've got Jack; Dan Gosling's done very well for us in recent weeks."
Bournemouth, who are 11th in the league, have picked up two victories in their 15 games on the road ahead of their Anfield trip.
(Reporting by Hardik Vyas in Bengaluru)
