In my research, I have found that this is just a rumour circulating many websites that are not reputable. While Elon Musk has a reputation of being interested in fertility and pushing the boundaries of our technology, there is no credible evidence that this is a project he is actively working on.
For a primary source, I went to the Musk-run Tesla website and found all of his publically available projects across all companies. He is working on technology that would link a human brain to computers, but there has been no mention otherwise of technology that would replace a biological function.
Source: https://www.tesla.com/elon-musk
For my secondary source, PolitiFact, a very reputable fact-checking website, published the article "Claims Elon Musk is developing a surrogate robot are unfounded," published October 29, 2024. In this article, the author, Ciara O'Rourke, investigated all claims that Musk was developing a pregnancy robot, but found that they were the result of a popular meme after a technological conference Musk talked at implied that robots he was developing could do "anything" for you. The source for this claim originated from internet users on Facebook and was flagged by Meta as misinformation.
My other secondary source is a reputable fact-checking website named Snopes, which also rated this claim false for the same reasons as Politifact. Published on October 31, 2024, "Musk Developing Robots to Carry Human Babies?" by Joey Esposito also delves into the claims and proves that they are all based off of internet memes and speculation.
As well, none of my secondary sources could find any credible source to prove that this was a project that Musk had announced he'd be working on.
Source 1: https://www.politifact.com/article/2018/feb/12/principles-truth-o-meter-politifacts-methodology-i/
Source 2: https://www.snopes.com/fact-check/musk-robots-human-babies/
Politifact discloses every part of their process, including their acceptance of financial donations with very specific guidelines. As well, Politifact states on their website that they do not "give donors, advertisers or grantmakers any influence over content or ratings. Our contracts and grant agreements have clauses asserting our editorial independence."
Source: https://www.politifact.com/article/2018/feb/12/principles-truth-o-meter-politifacts-methodology-i/#Our%20funding
As well, Snopes posts their funding/transparency about their donors and methodology on their website. There is a clear, well-researched process into publishing an article.
Source: https://www.snopes.com/disclosures/
Tesla's website has the potential to be incorrect if Musk is secretly working on this project, but as far as this claim goes, there is no credible evidence to suggest that Musk is working on this project publically.