Artificial-intelligence start-up Anthropic is in preliminary discussions with investors in the Middle East to raise between $3 billion and $5 billion in new capital at a valuation exceeding $150 billion, according to people familiar with the talks. The target price tag would more than double the San Francisco-based company’s present $61.5 billion valuation. Anthropic last raised $3.5 billion in March, financing that brought in Amazon, Google, Microsoft and Nvidia and underscored intensifying competition with OpenAI to develop large language models. Engaging Gulf sovereign wealth funds would mark a shift for the company, which had previously avoided such backers, and could give it deeper pockets to fund the costly computing infrastructure required for advanced AI systems.