Williams would fill the spot left vacant since the death of Virgil Abloh from cancer in November 2021, according to reports in the Wall Street Journal and Le Figaro.
They cited sources with knowledge of the talks, but Louis Vuitton's parent company LVMH has yet to confirm the news.
The 49-year-old is an established superstar in the music world, with 13 Grammys and two Oscar nominations, and he has been a fixture in the front row of fashion shows for many years.
Louis Vuitton's sales have soared since the pandemic, with the company now worth more than $20 billion -- helping to turn the owner of its parent company LVMH, Bernard Arnault, into the world's richest person.
The French brand had been happy to keep coasting on the hype generated by Abloh's three-year tenure, using his team and guest designers for recent shows.
Williams, who came to fame in the 1990s as part of hip-hop group The Neptunes, was not often mentioned in the rumors around the succession, but would fit perfectly with the label's recent moves to attract a younger streetwear-focused audience.
He has teamed with many fashion brands for individual lines, including Diesel, Chanel, Moncler and Adidas.
He partnered with Louis Vuitton in 2008 under then-creative director Marc Jacobs for a jewelery and sunglasses line.