"I'd sew the hems of his pants if he asked me to," the actress, 22, says in the April issue of Vogue.
Allen, 71, in turn describes Johansson as "criminally sexy," telling the magazine: "While she is a much stronger actress in every way, there is a tiny bit of Marilyn Monroe in her zaftig humidity."
Though Johansson – whose new movie The Nanny Diaries opens April 20 – plays Justin Timberlake's love interest in his "What Goes Around" video, she again denies rumors that they were ever an item.
"Of course it's not true," Johansson tells interviewer Alessandra Stanley. "We had fun together, but it's not like the first time I've ever hung out with him."
CRAIG McDEAN / VOGUE