Twitter's board reportedly met Elon Musk over the weekend to explore his $43bn (£33.6bn) takeover offer for the social media platform.
After the Tesla boss first revealed his bid, Twitter's management announced a so-called "poison pill" strategy to fend off a potential hostile buyout.
Mr Musk plans to finance his bid with the backing of US lender Morgan Stanley and other financial institutions.
A spokesperson for Twitter declined to comment on the reports.
Details of how Mr Musk intended to finance his offer, which were disclosed to US regulators on Thursday, made Twitter's 11-member board seriously consider a possible deal, according to Reuters, the New York Times and Bloomberg - citing anonymous sources.
Mr Musk, who owns a more than 9% stake in Twitter, has lined up a $46.5bn financing package for his bid, according to a regulatory filing.
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