The 43-year-old actress bonded with the animal when shooting `Wanderlust` - in which she plays one-half of a couple who turn their backs on their hectic New York lives to live in a hippy commune - and she particularly enjoyed milking the beast.
She said: "When we were doing our screen test, I met that goat because I had never milked a goat in my life, isn`t that weird? I`ve never milked a goat, I grew up in New York City, but I fell in love with our goat!"
Jennifer - who is dating actor Justin Theroux - could relate to her character as she loves taking a break from her regular life and career, but wouldn`t want to ever live in a commune.
Speaking on UK TV show `Daybreak`, she added: "Getting away is always something I love to do, of course, but the commune I think is a little extreme."
Jennifer`s co-star Paul Rudd jokingly claimed that part of the appeal of `Wanderlust` appeal is the number of "dangly bits" on show.
He said: "You can`t have a commune without dangly bits. If I`ve said it once, I`ve said it a hundred times."