The match is set to go ahead after referee Chris Foy declared himself happy with the pitch following an inspection despite snow in the area.
Terry has made just one brief substitute appearance since suffering a knee injury against Liverpool and was an unused replacement for the draw with Southampton last week and Sunday’s victory over Arsenal.
Nigeria duo John Obi Mikel and Victor Moses are at the Africa Cup of Nations while long-term absentee Oriol Romeu (knee) remains sidelined.
Swansea centre-half Chico Flores has recovered from a knee injury and is fit to return for the Liberty Stadium clash as the home side target a place in their first major cup final.
Gerhard Tremmel will return in goal having started in all previous rounds of the competition but midfielder Kemy Agustien remains sidelined with an ankle problem.
Swansea, who lead 2-0 from the first leg, will play League Two giantkillers Bradford City in the final at Wembley on 24 February if they overcome the Londoners.