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.