Musk said in the meeting he wants to encrypt DMs for security and add voice and video chat functions.
The creator of messaging app Signal, a former Twitter employee, could help with the plans, Musk said.
Under the plans, DMs would be encrypted, meaning the text could only be read by participants, as is the case on platforms like WhatsApp, Telegram, and Signal.
Musk added that he had spoken with the creator of Signal, Moxie Marlinspike, an ex-Twitter employee, who is "potentially willing to help out" with encrypting Twitter DMs.
In August, an ex-employee was found guilty of spying after passing Twitter users' information to Saudi Arabia, having been paid over $300,000 to do so.