Neither the Nationals nor Scherzer's agent immediately responded to requests for comment Sunday night.
Scherzer, a 30-year-old right-hander, is a free agent after spending the last five seasons with the Detroit Tigers. He turned down an offer from Detroit last March that would have paid him $144 million from 2015-20.
He was 18-5 with a 3.15 earned-run average in 2014, a year after going 21-3 with a 2.90 ERA and being voted the best pitcher in the American League. The NL East champion Nationals' starting rotation already includes Stephen Strasburg, Jordan Zimmermann, Doug Fister, Gio Gonzalez and Tanner Roark.
Blanco, Giants agree to deal
Outfielder Gregor Blanco and the San Francisco Giants reached agreement on a $7.5-million, two-year contract to avoid arbitration, a person with knowledge of the deal said.
Blanco will earn $3.6 million in salary this season and $3.9 million for 2016. The person spoke on condition of anonymity because the team hadn't made a formal announcement.
The 31-year-old Blanco could share time in left field after the defending World Series champions reached a $4.7-million, one-year contract with Nori Aoki on Friday.
Blanco has played at least 141 games in each of his three seasons with San Francisco. He batted .260 in 146 games last season.