Move or arrange oneself in a comfortable and cozy position(verb)
WordNet. Princeton University. 2010.
Use "draw close" in a sentence
"That I am intriguing against the rightful succession, and that I, a gentile, have managed to draw close enough to King Hyrcanus and his family to be considered as a suitor for Queen Alexandra’s daughter."
"The sound of his voice made Maud quickly draw close to me, as for protection, and she rested one hand on my arm while we parleyed."