Both Wise and Poyet were eligible to play for Swindon, although neither man took to the field during their short reign at the County Ground, and the Robins will continue to hold their registration until the transfer window opens at the turn of the year.
Leeds' chief executive officer Shaun Harvey said: "We haven't registered them as players, and we wouldn't be in a position to do that until January 1 because of the transfer window.
"It's something we would be able to do at that stage if circumstances required it, but at this moment in time we have no intention of registering Dennis Wise and Gus Poyet as players for Leeds United."