Murray won gold in men's singles at the Olympics in 2012 one year before his stunning Wimbledon victory in 2013.
Murray would become the first British winner of the men's singles title since Fred Perry in 1936.
Murray would also win the US Open in 2012 before striking gold again in men's singles at the Olympics in 2016.
The Brit first topped the professional tennis rankings in November of 2016.
Murray has only contested three professional level tournaments this year; going 2-3.
Federer fell to the former teenage star and 20 year old Felix Auger-Aliassime of Canada 4-6, 6-3, 6-2 in round two at the Noventi Open in Halle, Germany.
Federer, ranked eight, has only competed in four professional tennis tournaments this year; going 5-3.
The Swiss withdrew from Roland Garros in Paris earlier this month after winning three matches following two knee operations.
The 39 year old Federer has won 20 grand slam singles men's titles including eight Wimbledon singles titles.
Federer first reached number one on the professional tennis tour in February of 2004.