The phrase "put the eye on somebody" could be perceived as intimidating or threatening. Therefore, it might be helpful to consider alternative ways to express this idea. Some possible synonyms could include to watch closely, to keep an eye on, to closely monitor, to scrutinize, to observe carefully, to spy on, to surveil, or to keep tabs on. Each of these phrases could convey a similar level of attention or focus without the potential negative connotations of putting the eye on someone. Ultimately, it is important to use language that is clear, precise, and respectful when discussing one's observations or surveillance of another person.