Ben Zobrist scores a run during the World Series. (Noah K. Murray-USA TODAY Sports)

NASHVILLE –Ben Zobrist, a versatile veteran who was one of the Nationals’ top free-agent targets, signed a four-year, $56-million deal with Chicago on Tuesday night despite slightly larger offers from Washington and San Francisco, a person familiar with the situation said.

Both the Nationals and Giants offered Zobrist $60 million over four years, the person said. The 34-year-old switch-hitting infielder-outfielder was reunited with Manager Joe Maddon, for whom he played in Tampa, and will play for a contender. The Nationals weren’t close in the sweepstakes because Zobrist didn’t feel as comfortable in the Nationals clubhouse, according to another person familiar with the situation.

General Manager Mike Rizzo spoke with Zobrist during the recruitment process but did not have a face-to-face conversation on Tuesday in Nashville. Before Zobrist reached an agreement with the Cubs, Rizzo said the Nationals had made a “nice hard push” for the veteran.

The Nationals will scour the market for a left-handed hitter. They have some interest in outfielder Gerardo Parra. Infielder Daniel Murphy is available  but is considered a defensive liability. Potential trade options include Yankees outfielder Brett Gardner and Pirates second baseman Neil Walker, a switch hitter.