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The 30-year-old Johnson converted 50 of 59 save opportunities in 2013, going 3-8 with a 2.94 ERA. He was tied with Atlanta's Craig Kimbrel for the major leagues saves lead.
Abad went 0-3 with a 3.35 ERA in 39 appearances for the Nationals last season. He spent 2010-12 with the Houston Astros and has a career record of 1-14 with a 4.56 ERA.
The deal would bring Hudson back to the Bay Area, where he pitched for the Oakland Athletics as a member of the "Big Three" with Mark Mulder and Barry Zito beginning in the late 1990s.