The Angels had a scout in Japan last week to watch Tanaka, who could cost the team a posting fee of $25 million, according to the paper.
Tanaka set a Japanese professional baseball record for consecutive victories in a season by winning his 21st straight decision last Friday.
Angels starters entered Tuesday with a 4.37 ERA, the eighth-worst mark in the majors, and Jason Vargas, Jerome Williams and Tommy Hanson all are scheduled to be free agents this offseason.
Tanaka improved to 21-0 with a complete-game win in the Rakuten Eagles’ 6-2 victory over the Orix Buffaloes. The previous record of 20 was set in 1957 by Kazuhisa Inao.
Source: ESPN.com news services