Molineux Stadium club want Anfield reject.
The 30-year-old will leave Merseyside this summer after failing to establish himself in the starting XI.
He only joined the Reds 12 months ago from Fulham along with manager Roy Hodgson.
But he then became a symbol for the poor run under Hodgson and came under attack from supporters for his performances.
Konchesky’s mother then blasted Liverpool fans on facebook, branding them ‘scouse scum’ for criticising her son.
The left-back was sent on-loan to Nottingham Forest but Wolves boss Mick McCarthy will give him a chance to stay in the Premier League, according to Sky Sports.
McCarthy is keen to bolster his defensive options and he has rekindled his interest in Konchesky, whom he tried to sign in January.
A number of other clubs are thought to be keeping tabs on Konchesky’s situation with Liverpool thought to be ready to offload the defender.
Meanwhile, Liverpool will have announced they will conclude their pre-season preparations with a friendly against Spanish side Valencia at Anfield on August 6.