Jurgen Klopp’s side have been linked with a move for Traore after they missed out on Timo Werner, who now looks set to sign for Chelsea.
Traore has improved dramatically this season under Nuno Espirito Santo, scoring six goals and providing 10 assists.
It is likely the 24-year-old would be available for significantly less than the £52million Chelsea are likely to have to fork out for Werner, with the CIES Football Observatory transfer value list valuing him at between £27m and £36m.
But Pulis, who was Traore’s manager at Middlesbrough before he switched to Wolves for £18m, has urged the forward to stay at Molineux so he can focus on earning a place in the Spain squad for next summer’s Euro 2020 finals.
“I think Adama always had the ability to play,” Pulis told Stats Perform News, reported by the Mirror.
“The big thing was his confidence. I think I probably caught him at the right time. He had gone and worked for a few managers who weren’t enamoured enough to play him on a regular basis.
“I obviously knew him as a West Brom manager watching [Aston] Villa, watched him in the reserves a few times. His pace and balance was just extraordinary.
“Going to Middlesbrough, he wasn’t in the team when I got there but I wanted to make him a focal point of the team. We did that and the biggest thing with him is that he grew in confidence and he started to believe in himself.
“I made him my best friend. He used to come in and make me a cup of coffee after lunch and we would sit down and watch videos.
“He became a friend and he knew he’d be first pick on the team sheet. And the team understood what we could get from him and what we couldn’t.
“Having said that, as the season progressed, he learned the other side of the game [defensive] as well.”
Pulis believes Traore has a similar situation at Wolves, where has a good relationship with the manager and feels respected.
“You meet people in life who are really, really good people, and Adama is a really good person,” said Pulis.
“You hope and pray those people get everything out of life that they possibly can.
“He’s gone to Wolves – we didn’t want to get rid of him at Middlesbrough, but the only problem was the finances… He went to the right club, stepped up and has murdered it.
“I think he can only get better. His temperament and personality is first class.
“His next step, I speak to him now and then, his next step is to get a place in the Spanish side.
“I’ll be quite content for him, and I said this to him, to settle down. He seems happy at Wolves. He’s playing under a manager that’s confident with him and gives the respect Adama needs.
“But Adama’s big challenge is seeing if he can get a place in the Spanish team and keep it.”