The holders will once again be relying on the assistance of newly crowned Wimbledon champion Novak Djokovic.
“Djokovic looks unbeatable this season, and despite facing a tricky away tie, his presence should be enough to see the Serbs safely into the semi-final,” said Coral spokesman Gary Burton.
Serbia face Sweden in an indoor arena in Halmstad at the weekend.
In the other quarter finals, Argentina take on Kazakhstan, Germany face France, while Spain travel to the USA.
**DAVIS CUP OUTRIGHT
5-2 (from 3-1) Serbia, Spain, 9-2 Argentina, 5-1 France, USA, 12-1 Germany, 40-1 Sweden, 66-1 Kazakhstan