Klopp is keen to sign Traore in order to bolster his squad and ease the heavy reliance on his front three of Roberto Firmino, Mohamed Salah and Sadio Mane.
Liverpool will have to battle Manchester United and Manchester City for the signature of the Spanish star.
Traore has been a revelation at Molineux for the past two seasons.
He has scored six goals and provided seven assists for Nuno Espirito Santo’s side so far this season.
The 24-year-old joined Wolves from Middlesbrough in 2018 for £20 million.