According to MLB.com, the team made an eight-year, $160 million offer to free-agent first baseman Mark Teixeira.
The Los Angeles Times reported on Wednesday that the Baltimore Orioles have also made an offer to Teixeira, believed to be for seven years and about $150 million.
The newspaper also reported that the Angels have given agent Scott Boras the parameters of a deal to bring back Teixeira.
"Scott knows where we stand," Angels general manager Tony Reagins said, according to the Times. "We have a level of salary and years that we're comfortable with, and hopefully that will get it done. . . . If it doesn't, we'll have to move on."
Foxsports.com reported on Wednesday that the Red Sox were making headway in talks to sign Teixeira and that he was their No. 1 priority this offseason.
The Nationals finished 28th in the league last season in runs scored, 26th in batting average and 28th in home runs. Teixeira batted .321 with 33 home runs and 121 RBIs for the Atlanta Braves and Angels.
The Nationals went 59-102 last year and finished last in the NL East. After being traded by the Braves at the deadline, Teixeira helped the Angels run away to the AL West crown.
In the first postseason experience of his six-year career, Teixeira batted .467 in the ALDS, but the Angels lost in four games to the Red Sox.