This is the 2267th most frequent Japanese word.
近づい
The term "近づい" is a conjugated form of the verb "近づく" (chikazuku), meaning "to approach" or "to get closer."
The word "近づいて" (chikadzuite) here is used to describe the act of coming closer or approaching someone.
彼が私に近づいてきた。
He approached me.
"近づいている" (chikadzuiteiru) indicates the notion of an event or a time point coming closer in a metaphorical sense.
試験の日がだんだん近づいている。
The day of the exam is gradually approaching.
"近づいている" (chikadzuiteiru) is employed to express the subjective perception of something ominous or consequential coming near.