"Sir was like, man, come out the gate. He carries himself like that. He just came out, like, Sir," the rapper said.
Jay Z also made sure his upcoming tour for his brand new album 4:44 was scheduled long after their birth.
The whole family will hit the road in October.
"I booked the tour for October so I could have at least four months to just really bond and see their fingers and s**t like that," he said.
"They'll be with me [on tour] anyway but I'm just saying, like, [I needed] a space where I'm not doing anything. I'm just focused on them. I'm not thinking about a show at night or anything like that. That's why the tour is so far away from the release of the album," he added.
While the couple are yet to officially explain the name Blue Ivy, Rumi and Sir's five-year-old sister, a post from Beyonce in 2012 alluded to their reasoning.
Taking to Tumblr, Beyonce posted a passage from Rebecca Solnit's 2005 novel A Field Guide To Getting Lost which focused on the colour blue.
"The world is blue at its edges and in its depths. The blue is the light that got lost," it began.
The passage went on before ending, "The light that gets lost, gives us the beauty of the world, so much of which is in the colour blue".
