The move is effective from May 31 with the channels to be replaced by other high definition options.
Mark Cuban, owner of HDNet and the Dallas Mavericks NBA basketball team, wouldn’t comment "on ongoing negotiations" but refuted the claim that HDNet’s programming lacked appeal.
However, Time Warner Cable’s head of PR, Robyn Watson, said: "There’s a limited appeal for the programming.
"In a world with more than 100 HD channels, being in HD is not enough.
"We are adding other channels in HD to give our customers more choice."
HDNet remains widely distributed on US cable, and DTH satellite.
It brings viewers 20 hours of HD programming weekly, including its flagship news programming Dan Rather Reports and HD World Report.