Cahill has been a key figure in Chelsea’s defence this season, playing in a three-man defensive unit with Cesar Azpilicueta and David Luiz, but the on-field skipper is out of the Wembley tie following gastroenteritis.
Terry has not started in the Premier League - where Chelsea hold a four-point lead over Spurs with six games remaining - since September.
Former England international Terry this week announced his 22-year stay at Chelsea will end. Five of the 36-year-old’s 14 trophies were FA Cup wins.
Terry, who made his 713th and most recent appearance in the fifth-round win at Wolves in February, cited a wish to keep playing for his decision to leave Stamford Bridge at the end of this season, Conte said.
Nathan Ake is to replace Cahill on the left of defence against Spurs, with Conte insisting Terry is more suited to the central position in the back three, where Luiz is first choice.
“There is only one captain in Chelsea now and it is John Terry, if he plays or doesn’t play,” Conte said.
“(But) we have to find a new captain, and this is another problem that I have to solve.
“In this system the right position (for Terry) is in the middle of the three central defenders.
“If something happens to David Luiz, for sure the player with the right characteristics to play in this position is John.
“(But) in this case I think for this position Ake has the right characteristic to be the substitute for Gary.”
Kurt Zouma is Azpilicueta’s deputy, Conte said.
Conte insisted the result of the FA Cup clash was irrelevant to the Premier League - “I don’t think if one team wins or loses it can affect the other competition,” he said - but rebuked Mauricio Pochettino for apparently preparing an “excuse”.
Pochettino on Thursday said his side were underdogs, but Conte disagrees.
“There is a moment you have to finish considering yourself an underdog. I think this is the right moment,” the Italian said.
“Tottenham now is a really great power in English football. This is the third year for them (under Pochettino) and I think it’s the right moment to finish (talking about being) considered (an) underdog and to find his excuse.”
Chelsea’s Premier League lead was cut to four points by last Sunday’s loss to Jose Mourinho’s Manchester United.
And Conte must juggle the bid to reach the FA Cup final with his side’s title charge, which resumes against Southampton next Tuesday and then takes the Blues to Everton in what is a crucial week.
“This week is very heavy for us and I think it’s very important for us.
“I have to take the best decision, to find the right balance.”
Conte has shelved all distractions to focus on the season finale, insisting Chelsea would have been delighted to be in the current scenario if it was offered when he joined the club.
He added: “We have to enjoy this moment. Because this moment is great for everyone: for me, that is the first season; for my players, because they worked a lot to arrive at this point in the season and to have this type of game.
“If we think where we started this season, I think every one of us signed to have this situation now.”
Cahill trained on his own at Chelsea’s Cobham training base yesterday, but Conte said it was “impossible” for the England defender to play.
Goalkeeper Thibaut Courtois, though, is back following an ankle injury and left wing-back Marcos Alonso is also expected to be fit following illness.
Striker Diego Costa has not scored in six games, since the win at West Ham.
Conte is not unduly concerned, saying: “He is keeping the goals for the finale of the season. It is the right moment to score.”