The Cubs would not confirm or comment on the report.
Fujikawa, 32, played 12 seasons with the Hanshin Tigers, totaling 220 saves, and a 1.77 ERA. Last season, he appeared in 47 2/3 innings and compiled a 1.32 ERA. He was sidelined with an adductor strain and has not thrown 70 innings in a single season since 2007.
According to Rosenthal, the right-hander will receive a signing bonus of $1 million and $4 million in salaries in 2013 and '14. There is a vesting option valued at $5.5 million or $6 million, to be determined by games finished.
On Friday, Cubs general manager Jed Hoyer did confirm that he met with Fujikawa about 10 days ago and that the Japanese pitcher toured Wrigley Field. Hoyer said they were "very impressed" by the right-hander, but would not comment on a time-table or the negotiations.
The Cubs did re-sign set-up pitcher Shawn Camp, but otherwise have not made any additions to the bullpen.
"If we bring in someone who has closing experience, or a number of guys who have closing experience, that's no knock on Carlos [Marmol]," Hoyer said of the Cubs' current closer. "I think every team in baseball wants to have an assortment of guys back there who, if the need arises, can pitch in the ninth inning. Hopefully we can do that."
The Angels, Dodgers, Diamondbacks and Orioles also were believed to be interested in Fujikawa, who pitched in the 2006 and '09 World Baseball Classic as well as the '08 Beijing Olympics. The Angels recently signed Ryan Madson to be their closer, and would appear to be out of the mix for Fujikawa.
Last month, the Cubs were close to completing a deal with the Angels which would've sent Marmol to Anaheim for starter Dan Haren. The Cubs pulled that trade off the table because of concerns over Haren's medical reports. Marmol is entering the last year of his contract, and owed $9.8 million in 2013.
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.