The proposal was presented during ongoing discussions with Scott Boras, Teixeira's agent, at the Bellagio in Las Vegas during the Winter Meetings. Angels owner Arte Moreno met with Boras in the agent's suite on Tuesday, and Reagins has been in steady contact with Boras.
"It was made during our conversations at the Winter Meetings," Reagins told MLB.com. "We have a proposal in place for eight years. The specific dollar amount, I won't get into that."
The Angels had not intended to go to eight years, but the market apparently has forced their boldest move yet to retain Teixeira, the player they made their highest offseason priority from the moment he filed for free agency.
The bar has been firmly set at $20 million per year for Teixeira, the hottest property on the market. Boras initially said he was seeking a 10-year, $200 million contract for the slugger who began his career with the Rangers in 2003 and has 203 homers and 676 RBIs in six seasons with a .290 career average.
At 28, he is eight years younger than Manny Ramirez, who hasn't drawn nearly as much interest, but figures to get a lot more attention from clubs in search of offense after Teixeira signs.
The Nationals came forward on Wednesday with a reported $160 million offer across eight years for Teixeira. It is believed the Angels have at least matched that number.
"It's something they can consider -- or should consider," Reagins said, referring to Team Teixeira. "They have the right."
The Red Sox and Orioles also have made no secret of their desire to land Teixeira, and the Yankees also have expressed interest in the Maryland native when they haven't been rounding up the most expensive arms.
There has been widespread speculation that Teixeira, whose wife is from Atlanta, prefers to sign with an East Coast team. But the player has never confirmed that, and he left Angels management with the perception that he thoroughly enjoyed his three months with the club after arriving on July 29 from the Braves in exchange for Casey Kotchman and Minor League pitcher Steve Marek.
Teixeira, who will be 29 on April 11, flourished with the Angels, offensively and defensively.
Batting third in front of Vladimir Guerrero, he elevated the entire offense, hitting .358 with a .449 on-base percentage and a .632 slugging percentage.
Teixeira delivered 13 homers and 43 RBIs in 54 games for the Angels, reaching 30-plus homers and 100-plus RBIs for the fifth consecutive season with a combined 33 homers and 121 RBIs and batting .308.
He continued to swing a hot bat in the American League Division Series, hitting .467 with seven hits and four walks, but the Angels fell to the Red Sox in four games. It was Teixeira's first exposure to postseason play.
Boras cited winning, along with family comfort, among Teixeira's top priorities, and the Angels have won four division titles in the past five years.
"We're hopeful we can get this done and move forward," Reagins said. "In any case, we have a lot of work to do."
It already has been an eventful winter for the Angels, whose record-setting closer, Francisco Rodriguez, signed a three-year deal with a vesting option with the Mets. Outfielders Garret Anderson and Juan Rivera and starter Jon Garland are in the free-agent market.
The American League West champions are considering free agents and trade options with respect to adding pitching and offense. But everything continues to pivot around Teixeira.
"He's our guy," Moreno said, hoping to reel him in amid the stiff competition.
Lyle Spencer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.