"I'm guessing probably towards the end of this year should be good timing to find someone else to run the company," he told the World Government Summit conference in Dubai via video.
"I need to stabilise the organisation and make sure it's in a healthy place and that the product roadmap is clearly laid out... I think it should be in a stable position around the end of this year."
Musk paid $44 billion for his favourite social media platform and exiting day-to-day operations would allow him to deflect criticism that he is neglecting his other ventures, especially car company Tesla, which has seen its share price plummet since he took over Twitter.
Musk has given few clues to what type of leader he is looking for. On December 21, when he first announced he planned to step down as CEO, he said only that he would limit his own duties to software and server engineering once "someone foolish enough" had taken his place.
Since Musk took full ownership of Twitter on October 27, the platform has been riven by chaos, with mass layoffs, the return of banned accounts and the suspension of journalists critical of the South African-born billionaire.
Musk's takeover also saw a surge in racist or hateful tweets, drawing scrutiny from regulators and chasing away big advertisers, Twitter's primary source of revenue.
"It has been a rollercoaster," Musk told the Dubai conference.
Last week, thousands of Twitter users reported problems using the platform as the social network began letting paying users post tweets as long as 4,000 characters.
US tech media reported that Musk put out word to Twitter staff to put aside work on new features to focus on troubleshooting.
Despite the difficulties, the Twitter boss encouraged more communication.
"As a forum for communication, it's great. And I would just encourage more communication... to sort of speak in an authentic voice.
"Sometimes, people will have someone else be their sort of Twitter manager or something like that. People should just do their own tweets... I think that's the way to do it."
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