Sponichi is reporting that Yusei Kikuchi could announce his intentions as early as the 23rd.
"Japanese teams will get their shot on the the 16th and 17th and the Majors will have from the 19th to the 21st or 22nd," said Hanamaki Higashi baseball head Sasuga. "Kikuchi will make his decision once all the meetings are done."
It also seems like Kikuchi will be meeting with about 15 teams:
All the NPB teams other than the Giants (11)
New York Mets
Los Angeles Dodgers
San Francisco Giants
=== Update 10/14/2009 4:09pm
A Sanspo update provides this information:
It seems the Hanshin Tigers, Seibu Lions, Orix Buffaloes will meet with Kikuchi on the 16th. On the 17th, the Yakult Swallows, Chiba Lotte Marines, Rakuten Eagles, Hiroshima Carp, and Nippon Ham Fighters.
The Cleveland Indians will apparently meet with Kikuchi on the 20th.
=== Update 10/15/2009 12:05am
The numbers on the clubs appears to be changing. As of now, it appears Kikuchi will be meeting with 12 NPB teams and 8 MLB teams for a total of 20 teams.
10/16 - Seibu Lions, Hanshin Tigers, Orix Buffaloes, Yomiuri Giants
10/17 - the rest of the 8 remaining NPB team
10/19 - Los Angeles Dodgers, Boston Red Sox, and 2 other clubs
10/20 - New York Yankees, Seattle Marines, and 2 other clubs