Coach Michael Cheika admits he faces a tough decision over the captaincy but doesn't want to turn the situation into a "presidential run-off".
Brumbies veteran Moore was handed the Wallabies' armband by Ewen McKenzie earlier this year, only lasting a matter of minutes before suffering a season-ending knee injury against France.
Waratahs flanker Hooper has stepped in for the 13 tests since and, despite overseeing just five victories, Cheika is impressed with how the 23-year-old handled the role in a tumultuous period which included the Kurtley Beale text message scandal.
"It (the captaincy) is a strange situation because Stephen was picked to be captain by the previous regime and he lasted not long, which was unlucky for him," Cheika said.
"He's obviously got outstanding leadership qualities. He's going to be captain of the Brumbies next year so that's going to be held in a good stead.
"Hooper is not going to be captain of the Waratahs (behind incumbent Dave Dennis) but has captained them before and has captained here - that gives me a good option as well."
The Wallabies play only four tests before the World Cup in September and none before July, giving Cheika time to ponder his options, and the coach suggested Hooper had done enough to be the leading candidate.
"It's not going to be a presidential run-off or anything like that. It's going to be about just deciding what's best for the team at that time," Cheika said.
"Right now, I'll be truthful, I'm very happy with the job that Michael Hooper's doing."
Veteran playmaker Quade Cooper believes whoever takes the role will be leading a united squad of players who have developed a new "hard edge" during the spring tour.
Australia departed the UK on Sunday having lost three European tests for the first time since 2005 but Cooper insists the the changes implemented by Cheika have the team heading in the right direction.
"The results aren't what we wanted and the Australian public wanted but the fact is we're working harder than we ever have," Cooper said.
"You think back and think 'I used to work hard' and then you get pushed harder and you realise there's more you can improve on.
"What we've been getting out of how we've been training and pushing each other as teammates, that's going to put us in a good position next year."
