draw near vs draw close

draw near and draw close both are verbs.

Word	Noun	Adjective	Verb	Adverb
draw near	No	No	Yes	No
draw close	No	No	Yes	No

As verbs, draw near and draw close are synonyms defined as:

Other synonyms of draw near include approach, come near, come on, go up, near.

draw near (verb)	draw close (verb)
move towards	move or arrange oneself in a comfortable and cozy position
	pull towards oneself
	move towards