Slim, who controls traditional phone company Telefonos de Mexico, top Mexican cell phone carrier Telcel and its parent, America Movil, is worth $53.1 billion, compared with Buffet's $52.4 billion, Forbes said.
Buffet, the Berkshire Hathaway chief executive, was the world's second-richest man for the past seven years.
Slim, 67, is also close to passing Microsoft Corp. co-founder and Chairman Bill Gates, who is worth $56 billion. Gates, who co-founded Microsoft in 1975, has been the world's richest man for a record 13 years.
Slim's fortune has increased $4 billion since February, as key investment Carso Global Telecom jumped 15 percent, the magazine says. Carso holds stocks of companies including Slim's Telmex, Telcel and America Movil.
Slim's wealth -- in a country whose average income is $6,800 -- is the equivalent of roughly 7 percent of Mexico's annual economic output, the magazine said. Forbes estimated that if Gates had a similar proportion in the United States he would be worth $874 billion.