To my knowledge, there are no plans to move the moon, because it would require an incredibly large amount of energy. However, the orbit of the moon is changing all the time! The Earth's rate of spinning is gradually slowing down, and as it does the moon is gradually getting further away from the Earth at a rate of about 38mm per year. The energy of the Earth spinning is being transferred to the moon, causing it to speed up and be further away. You can relate it to a merry-go-round, where the moon is attached to the Earth that is spinning at the center.