Britain who topped Group B in the Davis Cup after their win over France on Sunday now face Serbia, as the draw for the Final 8 Knockout stage was announced on Tuesday.
Serbia finished second behind Czech Republic, but clinched their place in the Final 8 with a win over Spain.
Novak Djokovic beat Alejandro Davidovich Fokina just five days after winning the U.S. Open to help Serbia to a 3-0 win over Spain in Valencia.
Whoever comes out on top between Serbia and Britain will then face the winner of Italy v Netherlands in the semi-final.
Reigning Davis Cup champions Canada will continue their title defence against Finland, who came through as runners-up in Group D after surprise wins over Croatia and the United States, while Canada topped their group ahead of Italy.
The winner of Canada v Finland will take on either Czech Republic or Australia in the semi-final. Australia finished runners-up to Britain.