Twitter Inc. is in talks to sell itself to Elon Musk and might close a deal as soon as this week, a remarkable turn of events just 10 days after the billionaire launched his $43 billion bid for the social media giant, according to reports.

The two parties met on Sunday to discuss Musk's plan and were making progress, but there were still concerns to work out. There's no assurance they'll come to an agreement, according to the reports.

Following the announcement of the Tesla CEO's proposal, Twitter's management declared a "poison pill" strategy to stave against a hostile takeover.

According to a report by Bloomberg, the social media company is working out details of the deal and might strike an agreement as soon as Monday if discussions go smoothly.

After Musk announced a financing plan for the unsolicited proposal, which included backing from Morgan Stanley and other institutions, Twitter began to warm up to the idea of a possible acquisition.

Elon Musk had offered his “best and final” bid on April second week at $54.20 per share – which came to $41.39 billion – to “transform Twitter as a private company”.