The pair are said to have a running joke about Perry's love of the boyband, prompting Cole to send the comical gift ahead of her birthday later this month.
"Cheryl and Katy have become close since they appeared on The Graham Norton Show," a source told The Sun.
"Cheryl's been busy with her tour so she wanted to make sure she sent a present well in advance and let Katy know she was thinking of her.
"She knows what a big fan Katy is of the boys and how she has a major crush on all five of them so she knew Katy would love the dolls."
Cole also bought Perry a gold cat charm for her favourite bracelet.
Perry has previously declared her love for One Direction, joking that they are "very cute" but "very illegal".
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