As told by Timbaland on Facebook in 2012:

Food for thought: Ya boy Jay-Z always used to come through the studio when I was working in New York City. So I said to him one day while he was sitting on the couch, ‘Yo I may got something for you.’ He said ‘Cool, where it at?’ So I played him the instrumental for ‘Party People.’ He bop his head said ‘Whooo!’ After [that] you just saw [him] mumbling, almost looking like he was possessed by something, then 15-20 minutes later he said ‘Yo I’m ready, can I go in the booth?’ I was like ‘Ready for what?’ He said, ‘You wanted 16 right?’ I said ‘Yeah, if you got it.’ He said ‘Yeah, I got it.”

The engineer played the track and [the verse] was his first take. No stopping, just pausing for the ad-libbing. Now, mind you, I’m sitting there like ‘Nah, no way, that had to be written!’ But then I thought ‘How [did he know] to go off that sound in [the] beat?’ He walks out and was like ‘Cool?’ I was like ‘Damn right [it was] cool!’ I just look at him like ‘Dude you think you’re good don’t you?’ He just replied with that famous laugh, and said ‘What else you got?’

So I played him this other beat and told him ‘Nah fool, I can’t put you on this one 'cause this is for Timbaland and Magoo.’ He said ‘Then nigga why did you play it?’ I said ‘Because I like to piss you off like that!’ I told him I was still working on my verse. He said ‘Play the track.’ This is no lie: he gets up, walks to the kitchen, grabs something to drink, and starts that mumbling again. I’m like ‘Why does this fool keep mumbling?’ Then out of nowhere you hear a loud ‘Whoooo!’ from him. I’m like ‘Whooo what?!’ He keeps mumbling after we loop the track for like 30 minutes. Around 45 minutes he said ‘Can I lay this?’ I said ‘Lay what?’ He said ‘Lay this verse!’ I said ‘Dummy, didn’t I just tell you this is for Timbaland and Magoo?!’ He said ‘[Don’t worry] I know this ain’t for me.’

He goes in and laid a verse that had nothing to do with him, but something about me. Then he said on the mic ‘Yo, how many verses you said you needed?’ I was like ‘What the hell is going on?!’ Me and my engineer Jimmy Douglass look at each other like ‘Wow!’ So, to make a long story short, he laid both verses, I learned them, and gave y’all [‘Indian Carpet’]. Now go back and listen to the lyrics. Just know that one of the greatest of all time will forever be Jay-Z.