There are several synonyms for the phrase "has no time for," including "avoids," "ignores," "disregards," "shuns," "spurns," "neglects," "overlooks," "dismisses," and "shrugs off." All of these terms suggest a lack of interest or willingness to engage with something or someone, whether due to a lack of time, emotional investment, or simple disinterest. While some might view these actions as negative, there are certainly instances where it is necessary to prioritize one's time and energy, and saying "I have no time for that" can be an assertive way to do so.