The Blues were thought to be targeting Atletico Madrid left-back Filipe Luis, yet negotiations with the player and the Spanish champions have been slow.
Jose Mourinho is desperate to get a replacement for Ashley Cole in and should his pursuit of the Rojiblancos ace end in disappointment, Rojo will be his next port of call.
The Argentine defender has starred for his nation during their run to the World Cup Final turning in a number of composed displays from the back.
Liverpool and Tottenham have also been linked with him, but Chelsea could blow the pair out of the water with their superior budget.
Sporting are known to be open to selling their man, after realising that keeping him in Portugal may be impossible.
£15m should be enough for Rojo, but the Lisbon giants could be open to negotiating due to financial worries.
The 24-year-old only moved to the Estadio Jose Alvalade in 2012 from Spartak Moscow, whom he joined the year before from Estudiantes in his homeland.