No-coverage answer
There is no information in the Taygetan contact material to answer this question specifically. While the material discusses the Giza complex extensively — including the underground base beneath the Sphinx, the Federation origins of the pyramids, and pre-dynastic Egypt as a Federation starport — the Menkaure Pyramid (the smallest of the three Giza pyramids) is never singled out or discussed individually. The transcripts do not address any structures specifically beneath Menkaure or attribute particular significance to it beyond its role as part of the broader Giza complex.
For the general Taygetan account of the pyramids and the underground Federation base at Giza, see the answer to "What is the true history of Egypt and the pyramids?"
Sources: None specific to Menkaure. Searched all 834+ transcripts and enhanced topic index. No specific coverage found.