Tanaka, 25, was 24-0 with a 1.27 ERA in 28 regular-season games with the Tohoku Rakuten Golden Eagles.
Major League Baseball and Nippon Professional Baseball were discussing potential changes to the posting-fee agreement. No matter what is decided, Tanaka may not fit in the Cubs' budget, especially with the Yankees and Dodgers reportedly interested in the right-hander.
Tanaka is the most sought-after Japanese pitcher since Yu Darvish signed with the Rangers prior to the 2012 season. Texas paid the Hokkaido Nippon Ham Fighters a $51.7 million posting fee and then signed Darvish to a six-year, $60 million contract.
The Cubs also have a pitcher whose name has been talked about this offseason, and that's Jeff Samardzija, who has been mentioned in trade rumors with the Nationals and D-backs.
"Teams will certainly inquire about him," Hoyer said. "He's really proved over the last two years that he has great stuff. He's a tough competitor."
The Cubs and Samardzija have talked about a possible long-term deal. The right-hander is under club control for two more seasons. He's coming off his first full season as a starter, and he was 8-13 with a 4.34 ERA and 214 strikeouts over 213 2/3 innings.
"There could be rumors," Hoyer said. "Jeff has the perfect mentality for that. He just doesn't pay attention. I think it's somewhat the nature of being in a big market. You are going to have your name out there."
The Cubs are in the market for pitching, hoping to add another starter and some bullpen help, including a closer, this offseason.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.