The World Series champion Red Sox made offers to Jacoby Ellsbury, Mike Napoli and Stephen Drew, while choosing not to make an offer to catcher Jarrod Saltalamacchia.
"In a vacuum, we'd like to have all of [our free agents] back," said Red Sox general manager Ben Cherington. "We'll just have to see how it goes, and we'll continue to talk to all of them and see how the market shapes out."
The Yankees made offers to Robinson Cano, Curtis Granderson and Hiroki Kuroda.
Cano and Ellsbury are expected to shape the free-agent market this offseason, with each likely to land a lucrative long-term contract. Neither is expected to accept Monday's qualifying offer.
Carlos Beltran, Shin-Soo Choo, Nelson Cruz, Ubaldo Jimenez, Brian McCann, Kendrys Morales and Ervin Santana were also presented with qualifying offers by their respective teams.
The deadline for teams to submit qualifying offers was 5 p.m. ET on Monday. The $14.1 million salary was determined by averaging the top 125 player salaries from the 2013 season -- the amount is the same regardless of the free agent. Each player has one week -- until 5 p.m. ET on Nov. 11 -- to accept the offer. If he accepts, the one-year deal is complete. If he rejects it, the team making the offer will receive a compensatory Draft pick between the first and second round (assuming the player signs elsewhere). All compensatory picks will be made between the first and second rounds, in reverse order of winning percentage.
Any team that signs a free agent who was extended a qualifying offer will relinquish its first-round pick. That pick doesn't go directly to the former team, however; it simply dissolves, and the first round gets shorter. The exception is that if the signing team's first pick is in the top 10, it will instead forfeit its next pick.
If a team signs multiple free agents who were extended qualifying offers, it keeps relinquishing its next-highest Draft pick. Only players who have been with a club for the entire 2013 season will be eligible for compensation.
Bartolo Colon, Grant Balfour, Bronson Arroyo and Josh Johnson were notables who did not receive an offer.
Last year, nine players were given qualifying offers and none accepted.