Former Australian foreign minister Alexander Downer says Australia and Indonesia will have to go through a process of relationship rehab to get back on track.
An apology would be the wrong thing as it would acknowledge Australia was spying on Indonesia's leaders in 2009, he said.
But with careful diplomacy, rehabilitation could be achieved in a matter of weeks.
AAP reports that Mr Downer, who was foreign minister during the Howard government, said Australia and Indonesia could put together some protocols which would not compromise Australia's intelligence activities.
As well, Prime Minister Tony Abbott was also keen to upgrade the intelligence relationship.
"That isn't going to offer the Indonesians everything they want here but it does seem to me that if (Prime Minister) Tony Abbott goes down this path, it offers a sense of goodwill in the field of intelligence," he told Sky News.
Mr Downer told Sky News that Mr Abbott, who has now responded to a letter from President Susilo Bambang Yudhoyono, would be working on diplomatic formulas which preserve the integrity of our intelligence services and contribute to rehabilitating the relationship.
"Both sides are going to have to try to rehabilitate this relationship because it's in both sides' interests," he said.
The ABC reports Indonesia suspended military and intelligence cooperation with Australia on Wednesday.
The phone tapping took place in 2009 - when Kevin Rudd (Labor) was prime minister.
Mr Abbott has replied to Mr Yudhoyono's letter, but did not reveal the details of his correspondence.
He said one of his priorities as prime minister was to maintain a strong relationship with Indonesia.
"President Yudhoyono ... has been a very good friend to Australia - one of the best friends we've ever had," Mr Abbott said on Thursday.
Labor comment
Deputy Opposition leader Tanya Plibersek said Mr Rudd could play a part in easing diplomatic tensions with Indonesia.
But Ms Plibersek is not sure whether the former prime minister, who has now left politics, would want to help.
''Any senior Australian like Kevin Rudd, who as former prime minister and former foreign minister, if they've got personal relationships with senior Indonesians, it does no harm to be talking in that personal context to them," she told ABC television.
Also, Mr Abbott had not helped the situation with his addresses to parliament, Ms Plibersek said.
Neither had the coalition's election policies of turning back asylum seeker boats and its failure to consult Indonesia.
"I am sure that we will get the relationship back on track but we need to do it quickly," she said.
