If any of the three sign a major league contract with another team, New York would receive draft-pick compensation in next year's amateur draft.
Under baseball's new labor contract, the qualifying offers replace the team agreeing to go to salary arbitration. A player has until Nov. 9 to accept the $13.3 million deal.
Soriano opted out of a $14 million salary for next year, preferring a $1.5 million buyout.
New York had 10 other players who became free agents: pitchers Mariano Rivera, Andy Pettitte, Freddy Garcia, Derek Lowe and Pedro Feliciano; outfielders Raul Ibanez, Ichiro Suzuki and Andruw Jones; catcher Russell Martin; and third baseman Eric Chavez.