Typical recovery time for Tommy John surgery is 12 to 18 months.
"I think it's progressing well at this point, and hopefully I can come back strong next year and be a part of the team," Fujikawa said through a translator.
Fujikawa, 33, said he's content to not rush his rehab, which is in the very early stages.
Fujikawa was 1-1 with a 5.25 ERA and .239 average against this season, striking out 14 in 12 innings and going 2-for-3 in save opportunities. He was in the closer's role before a strained right forearm landed him on the disabled list in April, but was impressive upon his return, posting a 1.17 ERA in seven appearances.
With closer Kevin Gregg a free agent following the season and no other ninth-inning option on the roster, Fujikawa said he hopes to be the Cubs' closer in 2014.
"That was a goal when I first came to this team, so hopefully I can come back strong and kind of work toward that goal when I am actually back pitching," said Fujikawa, who signed a two-year, $9.5 million deal with a vesting option for 2015 in December.
Fujikawa said he hopes fans hold onto Saturday's giveaway in anticipation of the day he's a ninth-inning regular at Wrigley Field.
"I can't pitch anymore this season, but hopefully I can come back strong next year," Fujikawa said. "Hopefully the fans that received the bobblehead will be happy that they kept it."