There, it describes him as possessing "a unique and incredibly timely understanding of the current geopolitical moment".
It also labels him "extremely intelligent, humorous, candid and charismatic".
The news comes amid growing tensions between Turnbull and the government he left behind.
On a visit to Indonesia, Turnbull warned against moving Australia's embassy to Israel.
At a conference there, Turnbull spoke about how angry Indonesia was about Australia's potential move of the embassy from Tel Aviv to Jerusalem.
Asked whether Turnbull would be sent on any further government trips, Morrison said "No".
Speakers represented by the Greater Talent Network include former Boston Police Department Commissioner Ed Davis, Grammy award-winner Paula Abdul, Pulitzer Prize-winning journalist Carl Bernstein and General Manager of the Golden State Warriors NBA team Bob Myers.
The agency also once represented US President Donald Trump.
Earlier this year, it was reported that Turnbull donated his entire A$528,000 salary to charity, so money is not an issue for him.
He earned his fortune long before taking Australia's top job. The former Rhodes scholar and Oxford University student established an investment banking firm in 1987.
He left 10 years later to become a managing director of Goldman Sachs Australia.
But it was one key investment that really inflated his bank balance.
In 1994, Turnbull made a A$500,000 investment in internet service provider OzEmail. In 1999, before the dotcom bubble burst, he sold it to Worldcom for A$60 million.
