Discussions are no longer ongoing, and it was unclear why they stalled, according to the report.
Twitter declined to comment on the report, while Clubhouse did not immediately respond to a request for comment.
San Francisco-based Clubhouse, whose invite-only app allows people to discuss varied topics in audio chatrooms, recently reported 10 million weekly active users.
It has seen its popularity surge after appearances by billionaires Elon Musk and Mark Zuckerberg, and as more people took to it during the COVID-19 pandemic.
Twitter has its own live audio feature, Spaces, which it aims to make available for all its users this month.