Konchesky is widely expected to leave Liverpool this summer with the player not figuring in Kenny Dalglish's long-term plans.
The full-back joined Liverpool from Fulham last summer, but following Dalglish's appointment as replacement for Roy Hodgson Konchesky was farmed out on loan to Nottingham Forest.
Wolves boss Mick McCarthy is a big admirer of Konchesky and saw a loan move for him collapse during the January transfer window. The Molineux side were keen to take the full-back on a temporary basis but having already played for Fulham and Liverpool last season he could only move on an emergency loan deal.
McCarthy is still keen to bolster his defensive options and he has rekindled his interest in Konchesky.
A number of other clubs are thought to be keeping tabs on Konchesky's situation with Liverpool thought to be ready to offload the left-back.