The competition moves to Wembley after Monday's match rounds off the quarter-finals and the 36-year-old Chelsea captain is out of contract at the end of the season.
Conte hopes it will not be the last time home fans will see Terry in FA Cup action, but cannot be sure as he reiterated a decision on his future would not be reached until the campaign is over.
"For John? I hope not – I don't know about this," he replied when asked about Terry at Friday's news conference.
"I prefer every situation – my situation, my players' situation – to be faced at the end of the season when it will be the right time for everyone.
"I repeat: John is doing great work this season, on and off the pitch. And, for me, he is very important because he is the captain.
"He is working very well on the pitch and helping me a lot in the changing room, transferring the right message. For sure, he is an important player for us."
Asked if Terry would play against United, Conte added: "I have to decide the starting XI and I will try to make the best decision for the team.
"We want to go into the next round, in the same way Manchester United do, so I will try and make the best decision for the team. It's normal."
Conte says he has yet to decide the team he will select for the match. #CFC— Chelsea FC (@ChelseaFC) March 10, 2017
Conte insisted there was no update on a potential new contract for him either after he was recently linked with a move to Inter.
"It's the same, the same situation," he said. "I think that now we must be focused on the present.
"I am the first to be focused on the present.
"Then, when the moment arrives to face every situation, then you talk with the club. It's normal, this. But, now, it's important to be focused."