The handset was manufactured by Taiwan's High Tech Computer (HTC), the Times said. HTC representatives in Taipei declined to comment on the report.
Several other Web sites are also reporting the Sept. 23 event, including Gizmodo, which is displaying what appears to be an announcement from T-Mobile.
HTC has already said it is developing a mobile phone developed around Android and plans to call the handset "Dream."
The handset maker may end up being first in the world to put out an Android-based mobile phone, but other companies are also developing handsets around Android, including Samsung Electronics.
HTC's Google handset is just over 5-inches long and 3-inches wide, with a keypad underneath the screen that either slides out or swivels out. The aim of the keypad is for easy e-mail, note-taking and writing Web addresses.
Internet navigational controls are situated below the screen on the handset.
Android is an open source software platform that includes an OS and is designed to take advantage of Internet services for mobility. The software could become a potent new rival to Windows Mobile and other handset operating systems. At the launch ceremony early this year, Google announced that over 30 companies had joined the Open Handset Alliance.