Bowell said the job will come with a semidetached tiny home -- water and electricity included -- with a garden and view of the Aegean Sea and a salary.
"The daily hours is that of a part time job (approx. 4 hours) and the salary reflects the fact that you get the house for free (with everything paid). All expenses for the cats will of course be paid incl. all veterinary care. You will be expected to take a cat to the vet in case of illness and therefore will need to be able to drive a manual car," the posting said.
Bowell included photos of some of the cats along with views of the house, garden and sea on the rescue's Facebook page.
Bowell and her husband, Richard, moved from Denmark to Syros in 2011.
The two told The Telegraph they found bony cats relying on scraps for food, injured and feral cats and kittens in trash bins when the first got to the island.
They started taking in strays and working with local veterinary staff, ultimately improving the health of the cats on the island.
According to The Telegraph, the couple is leaving for New York, where Richard Bowell will work with the United Nations.
The couple has recruited five volunteers to narrow down more than 3,000 applications. The best person for the job, according to the posting, is someone who is 45 or older, has veterinary experience, can enjoy being in their own company, and has experience with feral or non-sociable cats.
More information on the position, including how to get salary specifics and where to send an application and photo, is available at the God's Little People Cat Rescue Facebook page. Bowell is still going through applications and said it will take some time to pick the right person for the job.