The unusual offer is part of a marketing strategy being handled by US agency Maven Strategies, according to reports.
As part of the deal, rappers will not be offered an upfront fee, instead McDonald's will pay between $1 and $5 every time the song gets radio airplay.
It is reported that record labels, producers and artists have already been approached and are only being encouraged to mention the Big Mac product, rather than the McDonald's name itself.
Although it is up to artists to decide how to integrate Big Macs into their lyrics, it is understood McDonald's will have final approval.
It is hoped that several tracks featuring Big Macs will be released by the summer.
Previous work by Maven involving rap artists included integrating Seagram's Gin into five songs last year. Other brands that often get namechecked by rap artists -- sometimes even without the offer of payment -- include Courvoisier, Cristal and Motorola.
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