An insider told Bloomberg that Mr Tucker is looking to get the division's value up to around $100 billion following his appointment as the firm's chief executive officer.
Mr Tucker, who previously held the top post at Prudential, has been brought into the firm ahead of AIG launching an initial public offering (IPO) for AIA.
Robert Benmosche, the chief executive officer of AIG, said the IPO will be "ready to go in the coming months when market conditions are optimal", but refused to give any further details on a more precise timeframe.
Last month, two leading shareholders in Prudential called for the return of Mr Tucker to their company, reported the Financial Times.
They wanted him back to replace Tidjane Thiam following the collapse of Prudential's $35.5 billion bid to take over AIA.
By Asim Shah