His suggestions were rebuked by Ukraine, which is fighting back against the brutal Russian invasion and has vowed not to negotiate after Russia annexed four occupied Ukrainian regions following a sham referendum.
He also suggested that Ukraine should remain a neutral country. Ukraine officially applied to join NATO this year.
This morning, Eurasia Group — a political risk consultancy group — claimed Musk spoke to Putin before tweeting about his Ukraine peace plan, Vice reported.
Political scientist Ian Bremmer reportedly stated in a mailout to Eurasia Group subscribers that Musk had told him Putin was "prepared to negotiate", but only if certain preconditions were met.
These include that Crimea must be recognised as part of Russia, that Ukraine accept a form of permanent neutrality, and that Ukraine recognises Russia's annexation of Luhansk, Donetsk, Kherson and Zaporizhzhia.
Musk said that Putin told him these goals would be accomplished "no matter what" and warned of a nuclear strike if Ukrainian forces pushed south into Crimea, Mr Bremmer reportedly claimed.
The reported conversation matched closely with the suggestion he publicly made last week.
But Musk, the world's richest man - with an estimated net worth of about $300 billion (US$219 billion) - has shut down the report he spoke with Putin recently.
Musk was asked on Twitter, the social media platform he is in the process of acquiring, "Hi [Elon Musk[, is this true?"
Musk replied: "No, it is not. I have spoken to Putin only once and that was about 18 months ago. The subject matter was space."
Musk also recently suggested that Taiwan should become a "special administrative zone" of China.
The suggestion was met with furious backlash, with the billionaire accused of throwing Taiwan "under the bus".
