Swisher and Kuroda are the only two of the Yankees' six impending free agents expected to receive $13.3 million deals.
According to a source, the Yankees are likely to extend the offer to Swisher and Kuroda, but not to Suzuki, Ibanez, Pettitte or Martin.
Swisher, who is seeking a long-term deal, does not fit into the Yankees' plan to cut payroll to $189 million by 2014, and likely will reject the qualifying offer; Kuroda, who worked on a one-year, $10 million deal in 2012, might accept it, and the Yankees would like to have him back.
If Swisher declines his qualifying offer, as is expected, the Yankees will receive a sandwich pick in next year's draft and whomever ends up signing him will lose their top pick in the draft. New York is also expected to make a qualifying offer to closer Rafael Soriano, who opted out of the final year of his contract earlier this week.
Four other Yankees players -- outfielder Ichiro Suzuki, catcher Russell Martin, left-hander Andy Pettitte and outfielder Raul Ibanez -- were candidates for a qualifying offer but are unlikely to get one.