Wales head coach Gatland is continuing his recovery in New Zealand after suffering two broken heels when he fell from a ladder at his holiday home last month.
"I can assure you I am going to be right in a few weeks and be up and running around," Gatland told BBC Wales' Scrum V programme. "At this stage, I'll probably struggle to make Brisbane for the first Test. If I can be in Melbourne and Sydney for the second and third Tests, that will be great."
Rob Howley will be in caretaker charge for the trip Down Under, which features three Test match appointments with the Wallabies and a midweek game against the Canberra-based Brumbies.
Gatland has also been a long-time favourite to coach the British and Irish Lions in Australia next year, which remains the case, although no announcement has yet been made.
While Gatland is certain to miss Wales' first Test in Brisbane on June 9, he is aiming to link up with the squad in time for the second Test seven days later.
He has been in regular contact with Howley and Wales' coaching team since his accident.
Gatland said he wanted "just to go and have a little bit of an input, really, to support the coaches and players as much as anything". He went on: "I've spoken to the Lions, obviously. I think they are just waiting to have assurances that the injury is going to heal, that it's not going to be a hindrance in 12 months."
Wales play the Barbarians in Cardiff this weekend, when flanker Martyn Williams is expected to win his 100th cap.
An advance party of players, headed by assistant coach and defence specialist Shaun Edwards, are due to leave for Australia on Thursday, with the remaining group heading Down Under next Sunday.