Real are looking to loan the Frenchman until the end of the season in a deal worth £1.5.
"He had asked the manager about a possible move and we felt it right to let him talk to Real Madrid," West Ham CEO Scott Duxbury told the club's official site.
"I was first contacted by Madrid on Friday morning and after extensive negotiations we have agreed in principle a deal that would see them paying us a £1.5million fee to take Julien until the end of the season."
Duxbury revealed that the Spanish champions would also consider landing the 25-year-old's permanently in the summer.
"His long-term future would then be reviewed in the summer with a significant transfer fee payable should Madrid want to take up their option," he added.
"If Julien does go on loan, then we will look quickly to bring in a replacement."
Faubert joined West Ham from Bordeaux in June 2007, but his progress at Upton Park has been hampered by a series of injuries.