The club have been forced to wait until the turn of the year when they hope to assess the likelihood of returning to the Premier League.
Keeper Green will be free to speak to foreign clubs from January 1 as his contract expires next summer.
On hold: Goalkeeper Robert Green's contract expires next summer
West Ham currently lie fifth in the Championship and, according to The Sun, if promotion back to the Premier League looks likely, owners David Sullivan and David Gold will come to the negotiating table.
Green, 31, is enjoying a new lease of life under new boss Sam Allardyce and is happy at West Ham but was heavily linked with a move to Aston Villa in the summer.
Leading light: Carlton Cole will also have to wait to begin contract talks
Whether the former England keeper stays beyond this season depends on the club's finances.
Sullivan and Gold have been forced to shell out around ?40million extra just to keep the wages and bills paid this season following the drop.
Millwall 0 West Ham 0: Bentley sitter costs Hammers win over bitter rivalsFormer West Ham striker Savio reported missing by Interpol My Club blog: Bentley and Lansbury provide Big Sam perfect plan for MillwallEngland Under-21 sensation Lansbury hammers out new deal at Arsenal