He was born in the village of Drenova, near Korçë. Aleksander studied at a Greek school in his village. His father died when he was just thirteen. In 1885, Aleksander moved to Bucharest, Romania to join his brothers. There he was exposed to other Albanian writers and nationalists.
In 1904, Asdreni published his first collection of ninety-nine poems called Rreze dielli (Sun rays), dedicated to Skanderbeg, the Albanian national hero. His second ninety-nine poem collection, Ëndra e lotë (Dreams and tears) was publish in 1912 and was dedicated to Edith Durham. Asdreni's third collection, Psallme murgu (Psalms of a monk), came in 1930.
After a brief return to Albania in 1914, Aleksander returned to Romania and continued to take interest in the Albanian national movement. He visited Albania again in 1937, but he soon returned to Romania.
Aleksander Stavre Drenova died on December 11, 1947.