Schwarzer gave up on his dream of joining Arsenal in the January transfer window, choosing instead to be part of Hughes' Craven Cottage revolution.
The 38-year-old, whose previous deal expired at the end of the season, had reportedly been offered a player-coach role by the Gunners, who saw more than one bid rejected for the Australia star in the summer.
Hughes would also be willing to give Schwarzer his big break in coaching, saying: "If that's something he wants to pursue in the future, I would certainly be receptive to enabling him to possibly start his coaching career and see how it develops. That would be an option for him, I'm sure."
Source: PA