The Red Devils beat Manchester City 3-2 at the Etihad Stadium on Sunday to reach the next stage of the competition.
Meanwhile, Liverpool disposed of League One side Oldham Athletic 5-1 on Friday night to set up a clash with their perennial rivals.
"And people talk about United always getting lucky cup draws!!! Couldn't get much tougher. What a game to look forward to," the 32-year-old tweeted.
Owen spent eight years at Anfield before a high-profile move to Real Madrid in 2004.