Johnson's agent, Alan Nero, speaking from the Winter Meetings in Indianapolis, said the left-hander is currently spending time with his family in Arizona and could begin working out again soon.
Johnson, 46, is expected to make his decision in the next few weeks, Nero told the AP.
Johnson went 8-6 with a 4.88 ERA with the Giants this past season and became the 24th pitcher to reach the 300-win plateau in June. But Johnson missed two months because of a strained left shoulder and returned as a reliever in late September, posting a 6.23 ERA in five relief appearances.
The five-time Cy Young Award winner owns a career 303-166 record, a 3.29 ERA and 4,875 strikeouts across 22 big league seasons as a member of the Expos, Mariners, Astros, Diamondbacks, Yankees and Giants.
Rhett Bollinger is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.