Manrique was born in Arrecife, Lanzarote, and grew up in the area of San Ginés lagoon. He fought in the Spanish Civil War as a volunteer in the artillery unit on Franco's side. At age 23, he participated in his first exhibition in Arrecife. He attended the University of La Laguna, but transferred to Escuela Superior de Bellas Artes de San Fernando in Madrid for five years in 1945. With Nelson Rockefeller in 1964, he visited Houston and New York in the "Catherine Viviano" gallery.
Manrique had a major influence on the planning regulations in Lanzarote, when he recognised its tourist potential and lobbied successfully to encourage sympathetic development of tourism. One aspect of this is the lack of high rise hotels on the island. Those that are there are in keeping with the use of traditional colours in their exterior decoration.
Manrique died in a car accident at Tahíche, Teguise, very near the Fundación, his Lanzarote home, in 1992. He was aged 73.