The Padres reached deals with catcher John Baker and pitcher Edinson Volquez, and exchanged figures with pitchers Luke Gregerson, Clayton Richard and Headley.
The team offered Headley $7.075 million for 2013. Headley's representation countered with $10.3 million. Headley made $3.475 million last season, when he finished fifth in the National League MVP vote.
Headley had a monster season in 2012, winning his first Gold Glove and Silver Slugger awards, and knocking in an NL-best 115 runs. He also hit a career-best 31 home runs and was the NL Player of the Month in August and September.
Exchanging salary figures with arbitration-eligible players will not preclude the Padres from negotiating with Headley, but it is an indication that time is running out to settle such contracts outside an arbitration hearing.
Those hearings will begin Feb. 4 and run through the 20th. If a hearing is necessary, an arbiter, after hearing points raised by both the organization and player, will select the figure submitted by one of the parties. That decision is binding.
Gregerson, who on Thursday was named to Team USA's provisional roster for the World Baseball Classic, made $1.55 million in 2012. Last season he posted a 2.39 ERA in 77 games, with a career-best nine saves. The Padres offered him $2.875 million. He countered with $3.75 million.
Richard matched his career best in victories (14) last season. He went 14-14 with a 3.99 ERA and made all 33 starts, earning $2.705 million. He is seeking $5.55 million. The team offered $4.905 million.
Volquez, who will pitch for the Dominican Republic in the Classic, will make $5.725 million. Last season he made $2.2375 million. He went 11-11 with a 4.14 ERA in 32 starts, second only to Richard in victories and starts.
Baker, who will split catching duties with Nick Hundley to start the season, will make $930,000. A year ago he hit .238 in 63 games in a backup role and made $750,000.
Late on Thursday, the team agreed to terms with left-hander reliever Joe Thatcher ($1.35 million) and shortstop Everth Cabrera ($1.275) on deals for 2013.
On Wednesday the team avoided arbitration with outfielder Will Venable ($2.675 million).
In November the Padres and first baseman/outfielder Kyle Blanks avoided arbitration by agreeing to a $605,000 deal for 2013.