The phrase "close eye" can have several synonyms that convey the meaning of focusing, observing, or paying attention to something or someone intently. One such synonym is "keeping watch," which involves remaining vigilant and alert to ensure nothing goes amiss. "Surveillance" is another suitable synonym that connotes the act of monitoring someone or something closely, such as in a situation where security is paramount. "Scrutiny" is also a synonym for close eye, which suggests a thorough examination of something or someone to detect any flaws or issues that may require attention. Other synonyms for close eye include "careful observation," "diligent attention," and "meticulous scrutiny".