The 31-year-old, who was part of the Real squad when they won the Champions League in 2002, is a free agent after leaving French side Arles-Avingon.
In 2002 Hammers boss Sam Allardyce came close to signing Pavon for Bolton in 2007 but the move fell through and the Spaniard moved to Real Zaragoza.
Allardyce, who is keen to find a defender as Winston Reid is out for six weeks with a dislocated shoulder, has had loan enquiries for Manchester City's Nedum Onuoha and Arsenal's Sebastien Squillaci rebuffed.
Source: Daily_Mail
