Tuilagi, who missed the win over Scotland last weekend, has been declared fit for the clash in Dublin, but Catt has insisted that his spot is not guaranteed.
"It is always difficult but it is a great headache to have. From a team point of view you have three guys and each of them bring special attributes. It is great Billy has come along and performed the way he did against Scotland on his debut," Catt told reporters.
"Manu has been out of the game for three or four weeks. We will see how they all train and we will go accordingly from there.
"If the guys have performed exceptionally well on the weekend, the guys coming in need to make sure they have the tempo and up the intensity to really put their hands forward. That is what we want on Tuesday."
The 21-year-old has 17 England caps to his name.