Which phrase means to make someone interested?

The phrase "Capture your interest" effectively conveys the idea of making someone interested because it suggests an active and compelling action. To capture someone's interest means to grab or seize their attention in such a way that they become intrigued or invested in the subject or situation at hand. This aligns with the notion of sparking curiosity or enthusiasm, which is essential when trying to engage someone’s focus.

In contrast, the other phrases convey slightly different meanings. "Engage your interest" implies an ongoing interaction that maintains interest rather than initially creating it. "Offer your interest" suggests a proposal of interest, which does not inherently create engagement but rather presents a choice. "Maintain your interest" indicates keeping someone interested over time rather than the initial act of attracting their attention. Hence, "capture your interest" is the most direct expression of sparking someone's curiosity.