The midfielder saw his deal at The Hawthorns expire in June but has stayed at the club to recuperate from a knee operation.
Bilic – who believes Barry's experience will be a vital addition to his squad – has previously confirmed the former England international will be given a new deal once he has proven his fitness.
And he expects everything to become official in the coming weeks.
"Gareth has joined in our last couple of sessions," the Croatian said.
"It was a big injury for his knee and he’s been working hard every day.
"He has spent hours and hours in the gym which is mentally very demanding and exhausting.
“But he is a top professional. I didn’t know him before I came here but I knew of him from playing against him and managing against England.
“I heard a lot of good things about him, not only as a player but as a person.
“I am often in the gym so I see him every day doing that boring stuff and he is a great example for a young player.
“It’s a brilliant example for a young player to see him on a daily basis, a player like that who has done everything in his life and his professional career.
“To have that motivation and hunger at this stage of his career is unbelievable and it’s a gift for a young player.
“His touch and quality was never a question. You need five minutes to smile when you see it."
Asked whether he expects Barry to re-sign in the next few days, weeks or months, Bilic said: "It’s not months and it’s not days.
"He just now needs to get back in training to get that fitness and match fitness.
“It’s a few weeks probably."