Fujikawa, 32, would compete with Carlos Marmol for the Cubs' closer role if the deal is finalized. Marmol was nearly traded to the Los Angeles Angels earlier in the offseason, and the Angels were reportedly interested in Fujikawa as well.
Marmol could still be traded as the winter meeting commence in Nashville starting on Monday.
Fujikawa recorded 220 saves in 12 seasons playing for the Hanshin Tigers.
A major league scout told ESPNChicago.com that Fujikawa throws between 91-93 mph on a regular basis and has an outstanding breaking ball. The scout said he may fit as a quality setup man better than a closer.
ESPNChicago.com's Bruce Levine contributed to this report.