The Balearic Islands in the Western Mediterranean were not occupied until around 2200 BC. Although the two larger islands of Majorca and Minorca have many megalithic monuments, principally taulas and talayots, they have not, so far, been part of any Atlantis location theory. The only mention that I can find is the unsubstantiated claim by Frank Joseph[0104.66] that the early settlers were invaders from Atlantis.
*The island of Es Vedra off the west coast of Ibiza, the third largest of the Balearics, has had a number of imaginative myths, old and new, associated with it. It is supposed to be the birthplace of the goddess Tanit and the limestone on the island is alleged to have been used to build the Egyptian Pyramids. Then, for good measure, Es Vedra is also claimed to be a peak of the mountains of Atlantis!*
In 1911, Albert Gruhn proposed that Atlantis may have lain between the Balearics and Sardinia(a), while a century later the American nuclear engineer, Robert J. Tuttle, suggested[1148.301] the Balearics as a possible location when sea levels were lower and the archipelago was more extensive.
The most recent discovery of a prehistoric stone structure on Menorca was reported in the Spring 2016 edition of Popular Archaeology magazine(b).