Andy Murray overcame a slow start to beat Florian Mayer of Germany 1-6, 6-1, 6-1 Friday and become the first British man to reach the Italian Open semi-finals in the Open era.
The fourth-ranked Murray also showed good clay-court form in Monte Carlo last month, taking a set off Rafael Nadalin the semi-finals.
The last British man to reach the semi-finals was George Hughes in 1932, while the last British player to win the title at the Foro Italico was Virginia Wade in 1971.
Hughes was the only British man to win the tournament in 1931.
Djokovic is on a 36-match winning streak and could take the No 1 ranking from Nadal if he wins this tournament and Nadal fails to win his quarter-final against Marin Cilic.
In women's action, Australian Open runner-up Li Na of China beat Greta Arn of Hungary 6-3, 6-1. Na's semi-final opponent will be either defending French Open champion Francesca Schiavone or Sam Stosur.