The reports said that while nothing is guaranteed, the Honda-powered team could be ready to debut as soon as 2009.
Anderson was reportedly a Honda guest throughout the recent Montreal race weekend, meeting with team chiefs Ross Brawn and Nick Fry.
None of the parties wanted to comment, but sources close to Honda have apparently said that the Japanese manufacturer is ready to sell engines, gearboxes and KERS systems to the new team.
Anderson is said to be meeting with F1 chief executive Bernie Ecclestone in London this week.
The US outfit would be assisted by Honda's North American arm, as well as several backers from within the US, while Takuma Sato is favourite for the lead cockpit.
Portugal's Alvaro Parente, who made his F1 test debut in January as a prize for winning the 2007 World Series by Renault, was mentioned as a possibility for the other seat.
The reports said Anderson's F1 team could be announced officially in mid-summer. (GMM)