It is understood AIG have signed a five-year deal which includes logos on the All Blacks' shorts and shirt sleeves.
When pressed on a potential jersey deal with AIG, a spokesman said no further comment would be available.
The All Blacks jersey has been considered sacrosanct but Tew has been careful to not rule out selling space to an advertiser.
It would be hugely controversial if the NZRU decided to take up AIG's offer, and not only because it would break more than a century of tradition.
AIG was a sponsor of Premier League football club Manchester United and appeared on the team's shirts from 2006 to 2010 in a deal worth more than $100 million. However, the company was a victim of the global financial crisis and had to be bailed out four times by the United States government. It meant, effectively, that the US were United's main sponsor during the 2009-2010 season.
According to the United Kingdom's Daily Telegraph, that coincided with a warning from the company's security team to US-based employees to "avoid wearing any AIG apparel with the company insignia" as a result of growing hostility towards the company following revelations of bonuses paid to executives from bailout funds.
Such was the hatred towards the company from American taxpayers, it decided to change its name to Chartis, and only changed it back last week as public sentiment softened.
According to Reuters, chief Bob Benmosche told staff in a memo last week: "The increasingly positive sentiment toward AIG is a powerful asset."
The All Blacks have had a shirt sponsor in the past, with Steinlager emblazoned on the right side of the jersey during the mid-90s.
Currently, adidas have a small logo on the right breast, opposite the silver fern on the left.
Additional reporting: New Zealand Herald