If they are unable to sign Teixeira, the Nationals will look at free-agent outfielder/first baseman Adam Dunn, who has hit at least 40 home runs each of the past five years.
The team is looking for a first baseman because of Nick Johnson's history of injuries and Dmitri Young's health record.
The Nationals already took steps to improve their club before the Winter Meetings started when they acquired outfielder Josh Willingham and left-hander Scott Olsen in a trade with Florida in November. Since then, the Nationals have signed their share of Minor League free agents such as first baseman Matt Whitney.
While they are in Vegas, the Nationals are also looking for starting pitching and relief help. As far as the starters go, John Lannan and Olsen are the only pitchers who will likely have a spot in the rotation. Washington also needs a veteran starter who can teach the young pitchers how to win.
After trading Luis Ayala and Jon Rauch, the Nats are looking for setup men.
"We are at a time in our development that we need certain things," team president Stan Kasten said. "We are continuing to build aggressively. Since we have taken over the club 2 1/2 years ago, we dedicated [our resources] to building player development. We have said both internally and externally that now it's time to improve the team in Washington and that's what we are trying to do."
Trades and free agency are not the only things that will take place in Las Vegas.
On Monday, results of the pre-1943 and post-1942 Hall of Fame Veterans' Committee ballots will be announced at 1 p.m. ET.
The Ford C. Frick Award winner will be announced the next day. Joe Nuxhall and Jacques Doucet are candidates to win the award.
The Baseball Writers' Association of America's Spink Award winner will be announced at noon ET on Wednesday. This year's finalists are Bob Elliott of the Ottawa Citizen, the Sacramento Bee's Nick Peters and Dave Van Dyck of the Chicago Tribune.
That same day, there will be an announcement from Major League Baseball regarding the 2009 World Baseball Classic.
On the last day of the Winter Meetings, the Rule 5 Draft will take place. The Nationals are looking to acquire a diamond in the rough like they did when they selected catcher Jesus Flores in the 2006 Rule 5 Draft.