Kanye West has reportedly penned a lullaby for Jay Z's daughter Blue Ivy.

The Yeezus singer is known more for his rap lyrics and raunchy videos, but friends say he wanted to do something special for his close friend Jay.

Blue Ivy, the first child for Jay and his wife Beyoncé Knowles, turned two earlier this week and received a bundle of cards from Beyoncé's loyal fans.

"Kanye wanted to do something personal for his best friend's baby," an insider told British newspaper Daily Star.

"So he decided he would write and record a lullaby especially for her. It won't be released, it's just for Blue."

The 36-year-old star is trying his hand at a softer sound in a bid to help Blue go to sleep.

He no doubt has experience soothing young children as his fiancée Kim Kardashian gave birth to the couple's first child, daughter North, in June 2013.

But he hasn't moved too far away from his usual views, with the lullaby's lyrics being centred on success and achievement.

"It's really catchy and slow. Rather than the usual sweet dreams-themed lullaby songs, Kanye raps about how Blue Ivy and Nori will be mega powerful when they're older. It also mentions how him and Jay Z will work hard to make sure their girls have an easier path than they did," the source added.

Rumours have circulated that Beyoncé and Jay are keen to add to their brood, and 2014 could be the year that Blue gets a new sibling.

"The initial plan was for Beyoncé's album to drop in the New Year, But Jay Z wants next year to be all about baby making. The plan is to start trying just before Beyoncé's world tour ends in Lisbon," a source close to the couple told British magazine Heat.