The actress and her two daughters are staying at the apartment is while going through a divorce from Joe Jonas.
The news comes after Swift, who briefly dated Jonas in 2009, and Turner were spotted hanging out together in New York City on several occasions. Amid the outings, a source told ET that the two women "have always liked and respected each other."
"They are fans of each other and have been friends for a while," the source said. "Sophie doesn't care that Taylor dated Joe. It was so long ago and in the past. Taylor has a good time when she's with Sophie and they enjoyed some fun girl time together last night."
Turner's updated living situation comes amid her complicated custody battle with her Jonas Brothers ex. Jonas filed for divorce from Turner earlier this month, and the Game of Thrones star responded by filing a petition in a New York court to ask for the "immediate return" of their two daughters to the United Kingdom.