The Twins were finalizing a three-year, $21 million agreement with free agent outfielder Josh Willingham late Tuesday night, according to two people familiar with the negotiations.

Team officials would not confirm the deal, but they acknowledged having serious discussions with Willingham's agent Matt Sosnick while awaiting a final answer from Michael Cuddyer on their three-year, $24 million offer.

By agreeing with Willingham, pending a physical, the Twins knew they effectively would be closing the door on Cuddyer and fellow free agent outfielder Jason Kubel. Barring an unforeseen development, those two players will sign elsewhere, bringing the Twins three compensatory draft picks -- two for Cuddyer and one for Kubel.

With Willingham in the fold, making $7 million, the Twins' projected 25-man Opening Day payroll would move close to $96 million. General Manager Terry Ryan hopes to trim the payroll to $100 million, down from $113 million on Opening Day last season.

After Willingham signs, what little payroll room the Twins have left likely will be spent on pitching.

The Twins made their final offer to Cuddyer last week and patiently awaited a response until Tuesday, when Sosnick said his client was within 48 hours of making a final decision.

"I don't think you want to get on anybody's timetable but your own," Ryan said. "It's important that we make sure we do everything in our ability to try to get a person to play that position [right field] that we like."

The Twins have been determined to sign one of three free agents for right field: Cuddyer, Willingham or Kubel. They made little progress with Kubel, a lefthanded hitter who wouldn't balance the lineup quite like a righthanded hitter such as Willingham or Cuddyer could.

As much as the Twins have valued Cuddyer's leadership and versatility, their evaluators view Willingham as a close approximation.

Both are considered consummate professionals. Both will turn 33 before Opening Day. Both have limited range defensively in the outfield, though Cuddyer has a better arm.

Willingham batted .246 with 29 homers and 98 RBI for Oakland last season. Willingham had an .810 OPS (on-base-plus-slugging percentage), and Cuddyer's was .805.

Though he played shortstop in college, Willingham has played left field almost exclusively in the majors. Still, Sosnick said Willingham would have no problem moving to right field.

Willingham struck out in a career-high 26.6 percent of his at-bats last season, but the Twins believe that was because he kept trying to hit homers for the power-depleted A's.

Cleveland was linked to Willingham earlier in the offseason, but on Tuesday, Indians president Mark Shapiro responded to a question on Twitter (@MarkShapiro) saying, "Willingham's bat a perfect fit but defensive fit was not good."

The Twins plan to put Denard Span in center field with the speedy Ben Revere in left, so they can afford to have a little less range in right field.

If Willingham signed with the Twins, he'd be playing in a tough home run park, at Target Field, but the Oakland Coliseum has traditionally favored pitchers, too. Last season, Willingham hit 15 home runs at home and 14 on the road. Cuddyer led all Twins with 20 home runs, hitting 10 at home and 10 on the road.

The Rockies and Mariners were the remaining teams reportedly interested in Cuddyer.

In 1997, the Twins drafted Cuddyer out of high school and went through a protracted negotiation. They made an offer, gave him a deadline, and he refused, with plans to attend Florida State.

Thirty minutes later, the Twins called back offering more money and signed him to a $1.85 million bonus. On Tuesday night, the Twins gave Cuddyer another deadline, and this time there appeared to be no turning back.