The Australians are winless in their first two matches under returning coach Jones and face a mammoth task at the MCG next Saturday night against the unbeaten All Blacks.
With the second Test in Dunedin early next month, the Wallabies are looking to lift the prized trans-Tasman trophy for the first time since 2002, when Jones was in his first stint as coach.
Veteran flanker Hooper is still battling a calf injury that ruled him out of last weekend's loss to Argentina, with a decision to be made on him over the weekend.
"He wasn't able to train today and we'll need to make a medical assessment of him over the weekend and see whether he can participate in the game or not," Jones told reporters on Saturday.
"We've still got a week to go and calf injuries we tend to be more careful with their rehab than other injuries so medical staff are being pretty careful with him."
Jones revealed that star prop Taniela Tupou had returned from the Australia A clash in Tonga unwell and could only manage his first run with the Wallabies on Saturday.
"If he can get through some some good training early in the week then he may be available for selection," Jones said.
With Quade Cooper and Nic White in their 30s Jones was questioned about the lack of pace in his halves and also from inside centre Samu Kerevi.
He defended Cooper and Kerevi, saying they were tracking well for the Rugby World Cup, which gets underway in early September.
"We've got a number of players coming back from long-term injuries and then we know those players, as much as we like them to be at their best now, they're not going to be their best until the World Cup," the coach said.
"We' don't know where Quade's going to end up - he's still four games into returning from an Achilles tendon and Samu Kerevi is three or four games back from an ACL and they're serious injuries.
"So with better exposure, the quality training and rugby training over the next period of time, they're going to get a lot sharper."
Jones dropped fullback Tom Wright from his squad following the losses to South Africa and Argentina with Andrew Kellaway and Jordan Petaia in the mix to wear the No.15 jersey.
Utility back Reece Hodge and backrower Pete Samu were also selection casualties.
"We need to improve the team, we haven't been good enough in the first two games so I'm still searching for what our best team is, that's quite obvious," Jones said.
"I've only had the players for a short time and I need to find out what our best combinations are so Kellaway and Petaia are definitely options at 15 and both have trained there this week.
"These games, as important as they are and certainly against New Zealand and the Bledisloe Cup we treat them with the utmost importance, but I've got to find out who the best 33 is for Australia and this is part of the process."
