Kuroda may consider accepting the offer, coming off a strong debut season in the American League in which he earned $10 million. Kuroda, who turns 38 in February, was 16-11 with a 3.32 ERA in 33 regular-season starts.
His performance might entice clubs to offer a multiple-year deal, but Kuroda has said in the past that he prefers going from year to year, so the qualifying offer represents something of a healthy raise from the Yankees.
Appearing Friday on SiriusXM's MLB Network Radio program, Yankees pitching coach Larry Rothschild said that he believes "there's a high-percentage chance" that Kuroda will return to the Yankees if he continues to play in the United States.
"I think he enjoyed the experience," Rothschild said. "I think his decision, to some degree, is going to be: Is this the year for him to go back to Japan? He feels like he has a debt to the team in Japan that he played for [Hiroshima Toyo Carp], that he would like to pitch, I think, another year for them before he retires.
"Whenever that comes about, I think when he thinks he's ready to do that, that's what he's going to do. And if he's not, then I think we have a good chance to re-sign him and he'll play for us or, you know, possibly the Dodgers. I don't know."
The Yankees declined to make a qualifying offer to catcher Russell Martin, who might have accepted the $13.3 million figure after hitting .211 with 21 homers and 53 RBIs in 133 games.
The Yankees offered Martin a three-year extension in the $20 million range this spring and are thought to have interest in retaining Martin, who turns 30 in February, but not at that dollar value.
The matter of qualifying offers is new this season, thanks to changes in the Collective Bargaining Agreement. The $13.3 million figure represents the average of the previous year's top 125 free-agent salaries.
If Soriano, Swisher and Kuroda decline the offers, they could still re-sign with the Yankees at a different price. Should the players sign with another team, the Yankees receive a compensation pick made between the first and second rounds by reverse order of winning percentage, while the signing team loses its first-round pick.
The top 10 picks of the Draft are protected, so any team holding a top 10 pick forfeits its second-round selection if it signs a player who received a qualifying offer (the Pirates' No. 9 pick is safe, as it is compensation for failing to sign their first-round pick this year).