The Saints played several young players against Shrewsbury Town this week.
But with their fourth round game being against a Premier League rival, Hasenhuttl will name a stronger team.
Asked about the game and his potential team sheet by reporters, Hasenhuttl said: "As strong as possible.
"We know that it is a tough game, but hopefully also for them.
"This is the goal we have, to make it as difficult as possible."