Woodgate was released from his Middlesbrough contract at the end of their successful promotion season in the Championship last year.
He has spent four years at the Riverside but made just one appearance in the League Cup last year.
The 36-year-old is a Spanish speaker after his two injury-ravaged seasons in Real Madrid from 20004-2006 and is expected to concentrate his scouting on Spain and Portugal.
Both areas have become a steady source of young players to Liverpool, albeit with mixed success.
Woodgate is known to split his time between the UK and Ibiza though he has recently been acting as a club ambassador for Middlesbrough.