American Airlines with its partner Fort Worth-based TPG could invest more in the financially-struggling Japan Airlines than the $1.1 billion it has already proposed.

“Conceivably, there could be a bigger investment made by the oneworld-TPG group depending on the circumstances,” American Airlines chief executive Gerard Arpey told reporters in Tokyo on Wednesday.

Arpey was in Japan on Wednesday meeting with government officials and management of Japan Airlines. JAL has lost hundreds of millions of dollars this year and is seeking government loans as it cuts routes and tries to restructure.

And while JAL is currently part of American’s Oneworld alliance, it has been offered a $1 billion investment package from Delta Air Lines to switch to Delta’s SkyTeam alliance.

Arpey also said that if JAL continues its relationship with American, the Fort Worth-based airline would give JAL “exclusivity” and would not try to create alliances with other airlines in Northeast Asia that could compete with JAL’s network. He did not reveal any additional financial details of the investment proposal or how much is being funded by TPG, a private-equity group.

Last week, the U.S. and Japanese governments agreed to an “open-skies” treaty that relaxes limits on passenger and cargo flights that currently exist between the two countries.

If JAL chooses American’s proposal, American said it would apply for anti-trust immunity for its relationship with JAL. Anti-trust immunity would allow the two carriers to more closely market and operate flights.

In advocating his airline’s proposal, Arpey said choosing American’s “superior” proposal over Delta would help JAL in its goal for “long-term success.” He added that if Delta was chosen, he did not believe that U.S. government regulators would approve an anti-trust immunity venture between Delta and JAL.

“We would object loudly and stridently,” Arpey said. “I think there is zero possibility that that application would be approved.”