draw close vs nestle

draw close is not a noun while nestle is a noun.

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

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

draw close and nestle: move or arrange oneself in a comfortable and cozy position

Other synonyms of draw close include cuddle, nest, nuzzle, snuggle.

draw close (noun)	nestle (noun)
	a close and affectionate (and often prolonged) embrace

draw close (verb)	nestle (verb)
move or arrange oneself in a comfortable and cozy position	move or arrange oneself in a comfortable and cozy position
pull towards oneself	position comfortably
move towards	lie in a sheltered position