Which Manu currently rules?
The present reign is that of Vaivasvata Manu. According to astronomical calculations, we are now in the twenty-eighth yuga of Vaivasvata Manu. Each Manu lives for seventy-one yugas, and fourteen such Manus rule in one day of Lord Brahma. We are now in the period of Vaivasvata Manu, the seventh Manu, and the eighth Manu will come into existence after many millions of years. But Sukadeva Gosvami, having heard from authorities, foretells that the eighth Manu will be Savarni and that Nirmoka and Virajaska will be among his sons. Sastra can foretell what will happen millions and millions of years in the future. The total duration of the periods ruled by these Manus is calculated to be one thousand catur-yugas, or 4,300,000 times 1,000 years. This is called a kalpa, or one day of Lord Brahma.
Source: A.C. Bhaktivedanta Swami Prabhupada (2014 edition), “Srimad Bhagavatam”, Eighth Canto, Chapter 13 – Text 11 and Introduction