Teixeira is expected to command a salary of at least $20 million per season over a period of eight to 10 years.
Though Red Sox general manager Theo Epstein doesn't discuss his status with individual free agents, he discussed the market in a broad sense before leaving Vegas.
"We're kind of still in the middle of the process," Epstein said. "Not at the end. We're just in the middle of the process with a lot of guys."
Epstein confirmed that he has made offers to three different free agents.
"There are a number of other guys we've kind of discussed parameters with," Epstein said. "It's kind of a fine line between offer and non-offer -- semantics."
Are offers still going back and forth between the Red Sox and any players?
"A little bit," Epstein said.
Without question, Teixeira is the one high-profile free agent Boston is aggressively focused on acquiring.
Though the Red Sox have been portrayed as the favorites for Teixeira in some media circles, Epstein remained even-keeled about the chances his club has of striking a major deal.
"We're optimistic about where we are as an organization and our foundation and the core elements," Epstein said. "As far as specific moves or adding certain players, until you get those things done, you can never be too optimistic."
While Teixeira is the most glamorous thing the Red Sox are working on, Epstein has several other issues on his plate.
An offer has been made to catcher Jason Varitek, Boston's captain the last four seasons. Whether or not Varitek returns, Epstein continues to look for ways to improve the team's catching situation for 2009.
Adding another starting pitcher remains a priority for Boston. John Smoltz is an intriguing name that has emerged in recent days, though it's still hard to imagine the veteran righty pitching anywhere but Atlanta.
Boston is also on the lookout for a fourth outfielder, preferably one who bats right-handed.
Deals done: The Red Sox didn't make any trades or signings during the Meetings. However, they did acquire reliever Ramon Ramirez in a trade for Coco Crisp in November. Boston also signed American League Most Valuable Player Dustin Pedroia to a six-year contract.
Rule 5 Draft activity: The Red Sox selected right-hander Miguel Gonzalez from the Angels. He projects as a reliever, though he also has experience starting.
Goal accomplished: Boston emerged as one of the front-runners for Teixeira, the most coveted free-agent hitter on the market.
Unfinished business: The Teixeira sweepstakes are ongoing. The catching situation remains unresolved. Will Varitek return? The Red Sox are believed to be the only team that has offered the veteran catcher a contract thus far. Epstein is still monitoring the trade market for a catcher who could either complement Varitek or replace him.
GM's bottom line: "It was productive. [There were] a lot of talks. Probably not the most efficient, not a model for how you would draw it up. But we're through it and made some progress in some fronts and we'll keep going." -- Epstein, on the Winter Meetings
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.