Stoke had a £12million offer for Shaqiri accepted last week but have so far been unable to complete a deal for the Switzerland international amid reports of interest from the likes of Atletico Madrid and Tottenham.
Bowen, however, is hopeful the transfer could yet take place, although he admits Stoke will have to look elsewhere if the 23-year-old does not put pen to paper soon.
“We are still waiting,” Bowen told The Sentinel. “There is a limit to how long we can wait, but we are hopeful and still waiting, it’s as simple as that.
“We know the qualities he’s got and maybe in January we got excited for a few days thinking we could bring that kind of player to Stoke. It didn’t happen then, but maybe it will happen now.
“The lad left Basel, went to Munich, and two-and-a-half years later he leaves there to go to Inter. Now it’s only six months later. Maybe he’s thinking whether he wants to move again or put down roots and stay in one place. That will be at the back of his mind, so you have to give a player like him the time.
“You can push, push, push, but there is a balance between doing that and giving him the time to make the right decision for himself. They have to want to sign.”
Stoke are also reported to be in talks to sign Glen Johnson on a free transfer after the right-back left Liverpool.