In a poll launched on the platform, he asked: "Should I step down as head...? I will abide by the results".
However, replying to one Twitter user's comment over who would then take the reins...
... Musk said: "There is no successor."
The billionaire, who also runs Tesla and Space X, bought Twitter in October.
This latest poll comes after Twitter announced a policy update on Sunday.
The company said it will remove accounts created solely for the purpose of promoting other social media platforms and content that contains links or usernames.
But cross-content posting from other sites will still be allowed.
The new measure would impact content from platforms like Facebook, Mastodon, Truth Social and Tribel.
Former Twitter CEO Jack Dorsey, who recently invested in social media platform Nostr, replied to the Twitter support post with one word: "Why?".
The policy change follows other chaotic actions at Twitter since Musk took over, including the firing of top management and indecision over how much to charge for Twitter's subscription service Twitter Blue.
On Friday, he reinstated several journalists' Twitter accounts he had suspended for allegedly sharing location data about him.
