Writing in The Australian, Ella opined that the Sydney-based Waratahs were a "big team in a big city and that requires a big-name coach."
Gibson's contract with the New South Wales Super Rugby franchise expires at the end of the 2020 season and Ella believes the current Wales coach would be ideally placed to take over.
"The word in Europe is that Gatland will not get the England job after the World Cup in Japan later this year, which means his only ongoing commitment will be coaching the British and Irish Lions in South Africa in 2021," Ella wrote.
"Gatland may prefer to return to his native New Zealand to coach Super Rugby, especially as he would have a greater chance of winning a title. But the Waratahs should sound him out, not just for themselves but in the national interest."
Ella, who played 25 tests for the Wallabies between 1980 and 1984, said Australia desperately needs an injection of experienced, international-standard coaching to lift playing standards.
"Australia has not had a serious Super Rugby title contender since the Waratahs won it in 2014. How long will it be before we have another champion team? Can we rely on the current crop of Super Rugby coaches to take us there?
"If you look at the inconsistent form of Australia's Super Rugby teams, none of them look like making a serious challenge this season. You might argue that New Zealand coaches have an advantage because their teams are more talented but if you have less playing talent, even more reason to emphasise coaching."
The Waratahs will lose current assistant coach Simon Cron at the end of the year, when he becomes head coach of Japanese Top League club Toyota Verblitz. All Blacks coach Steve Hansen is set to take a director of rugby role at the Japanese franchise after this year's World Cup.