Rugby Australia has yet to officially announce Jones' departure in the wake of the Wallabies' failure to reach the knockout stages of the Rugby World Cup, but McLennan vowed to continue in his role as he described the "sad Eddie situation" as a "hurdle we'll overcome".
The former England coach's departure just nine months into a five-year contract has been widely reported in Australia amid further speculation he is heading for a second spell in charge of Japan.
McLennan told the Sydney Morning Herald in a statement: "I came to rugby to find a way to fix it when it all fell over and despite the sad Eddie situation, this is another hurdle we'll overcome.
"I want to stay to deliver the 2027 World Cup in Australia. That has always been the big prize for Australian rugby.
"More destabilisation will just make matters worse, just when we're about to break through. Life is not a continuous line of perfect calls and success."
McLennan played a key role in bringing Jones back for a second stint in charge of Australia, the 63-year-old replacing Dave Rennie just a month after being sacked by England following five wins in 12 Tests in 2022.
But his return turned sour with just two wins in nine Tests - against Georgia and Portugal in the World Cup where they suffered losses to Fiji and Wales.
The failure to get out of the group stages for the first time came against a background of Jones denying he took part in an interview with the Japanese Rugby Football Union, both during and after the World Cup.
Despite multiple news outlets reporting that he was poised to meet officials in Japan next month for a second interview, Jones has repeatedly told the media that he was committed to Australian rugby.
Jones told the Sydney Morning Herald on Sunday: "(I) gave it a run. Hopefully be the catalyst for change.
"Sometimes you have to eat s**t for others to eat caviar further down the track."