Root enjoyed a successful first summer in charge of England, leading the team to series victories over South Africa and West Indies and scoring over 700 runs.
The Yorkshireman reverted to number four after replacing Alastair Cook as captain but there have been calls for Root to move back to No.3 this winter.
Tom Westley finished the summer in that position but was left out of England’s Ashes squad and James Vince is expected to come into the side.
But Gooch said: ‘I do think he [Joe Root] should bat at No 3 and the reason I say that is because we need to make a statement.
‘We cannot have a weak link, we cannot be 25-2 every time. In this line-up, he has to bat at No 3.
‘If we had a regular No 3 who was successful and had a track record behind him, then [Root] can bat at No 4, but I don’t see any of the players who are hopefully going to make a name for themselves [James Vince, Dawid Malan and Gary Ballance] batting there.
‘It’s going to be tough – Australia always target the captain, look to undermine him if they can.
‘If they can undermine his performance so he is not a big contributor in matches that undermines his well-being and confidence. Then, in theory, he might not lead the side so well.’
England are braced to take on Australia without star all-rounder Ben Stokes after he was arrested on suspicion of causing actual bodily harm last month.
The 26-year-old will not travel to Australia with the rest of the squad later this month and Gooch insists his absence would be a ‘great loss’.
‘I don’t think what’s happened over the last few weeks has helped England’s cause at all,’ Gooch added in an interview with Sky Sports.
The disruption this could cause is going to be difficult to cope with. Stokes is an influential player. He is our third best player, in my opinion.
‘He has a fantastic technique and has made so many improvements with his batting. He would be a great loss.’
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