Gregan, who will equal retired England prop forward Jason Leonard's world record of 114 Test appearances against the All Blacks in Auckland on Saturday, has been taking the brunt of the criticism for Australia's recent poor showing, which has seen them lose their last four Tests.
After making his international debut against Italy in 1994, Gregan has played in three World Cups, including the 1999 winning side.
But national coach Eddie Jones and ARU managing director and CEO Gary Flowers both gave Gregan their full backing on Monday.
Jones believes at this stage there is no reason why Gregan should not be selected on the Spring Tour.
"George has received an enormous amount of criticism over the last month, and in turn there has been considerable speculation on his position in the team and future in the game," Jones said.
"At this stage there is no reason why he would not be selected on the spring tour (to Europe).
"Like every player in the squad, his performance during the winter season will be reviewed and evaluated, but he is the current Australian captain and the right man to lead the team through this next period of time."
Jones said Gregan was remaining upbeat despite the criticism.
"George is resilient, it won't stick," he said.
Flowers said the speculation surrounding Gregan was disappointing for a player of his stature in the game.
"His leadership has been unquestionable since taking over the captaincy in 2001 and through this difficult period more recently, as well as over the next period of time, George is the right man to lead team," Flowers said.
Earlier, Gregan cast aside reports that he was to announce his international retirement during a radio interview.
He told ABC Radio: "That's just fictitious. That's got nothing to do with where I am at the moment."