Konchesky fell out with Curbs while at Charlton and was offloaded this summer from Upton Park, he told the People: "Curbishley has bought big players for West Ham, like Craig Bellamy, Matthew Upson and Freddie Ljungberg and his neck is on the line now.
"If the chairman isn't happy I don't think he'll hesitate to get rid of him, and it will be before Christmas if he wants to. The fans will make their opinions known, too.
"It is all very well the chairman claiming that the players were the problem, but I think that has come from the manager because the chairman didn't get involved with the players and he doesn't know us.
"It is easy to use us as scapegoats because we've left the club but whoever played gave 110 per cent and it is disappointing to read those comments, it hurts.
"The chairman needs to have a long, hard look at the manager. Okay, he has brought in new players, but they weren't the ones at the top of his wish list - he couldn't get those."