Cahill had a brief spell in hospital in the build-up to the Wembley semi after arriving at the club's Cobham training facility on Tuesday with "a bit of a fever" - symptoms which were later diagnosed as gastroenteritis.
"Not a serious problem, but now Gary is getting better and is improving a lot," Conte confirmed on Friday while declaring "impossible" his chance of featuring in the FA Cup tie.
The England international has started every Premier League game for Chelsea this season, lining up alongside David Luiz and Cesar Azpilicueta in a back three for much of the campaign.
But Conte must now shuffle his defensive pack and has suggested he will snub captain Terry in favour of Nathan Ake, who was recalled early from a season-long loan spell at Bournemouth in January.
Ake, 22, has made just two cup appearances for the Blues this season, but Conte said: "I think he’s a good player, I think he’s ready to have this opportunity, to have this chance, he deserves this opportunity and I trust him. I have no problem to take this decision.
"I think for this position Ake has the right characteristic to be the substitute for Gary."
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