When we are in close communication with someone, it means we are maintaining a close and frequent communication with them. There are several synonyms for the phrase "in close communication," including "in constant contact," "in regular communication," "in frequent communication," and "in regular touch." These phrases convey the idea that we maintain an ongoing, regular, and reliable line of communication with someone. Other synonyms that describe similar concepts include "in close contact," "in regular conversation," and "in regular dialogue." Regardless of the synonym used, the overarching concept is that we are maintaining a consistent and reliable line of communication with someone.