Matthew was released in January after serving more than 20 years of his 35-year sentence for non-violent drug and weapons charges, following the implementation of the First Step Act, a US prison reform bill, reports aceshowbiz.com.
The "Keeping Up with the Kardashians" star reached out to him privately and made the generous offer in an effort to get him back on his feet following his release.
Kim took to social media to appeal to her fans and followers to put her in touch with someone who could help the former prisoner.
In the post, she appealed to her followers on Twitter and Instagram for any landlords who knew of a two-bedroom apartment in Tennessee to e-mail her team.
"Matthew Charles's lease application was rejected again (because) of his criminal record (even with me paying his rent in advance)," she wrote.
"If there are any landlords (with) a two bedroom in Nashville willing to give Mr Charles a second chance, contact email@example.com."
"Serious inquiries only, thank you," Kim added.