The club declined to offer salary arbitration to catcher Jason Varitek, left-handed pitchers Erik Bedard and Trever Miller, right-handed pitcher Tim Wakefield, and outfielders J.D. Drew and Conor Jackson.
Ortiz and Wheeler will have until Dec. 7 to accept or decline arbitration. Under the terms of the collective bargaining agreement, clubs retain the right to negotiate and/or enter into a contract agreement with any of their free agents, regardless of whether arbitration was offered. There are no deadlines for such negotiations or agreements.
If Ortiz, a Type-A free agent, accepts a deal elsewhere, the Red Sox would receive two draft picks as compensation. That scenario could give other teams pause about signing the designated hitter and having to yield a first-round pick.
Red Sox general manager Ben Cherington admitted last week that he has had a lot of dialogue with Ortiz and his agent since the end of the season, and there seems to be mutual interest in getting a deal done so Ortiz will remain with the Red Sox.
"David knows we want him to be here, we want him to be back with the Red Sox and we want him in our lineup," Cherington said last week.
It's no secret that Ortiz, 35, wants to remain in Boston for the remainder of his career and would like a multiyear deal. He made $12.5 million this past season, finishing with a .309 average, 29 homers and 96 RBIs.
"If the Red Sox sign me they won't regret it," Ortiz told ESPNBoston.com last month. "I've got so many way to keep doing what I've been doing around here. I bring so much to this organization, I bring so much to the table here because I care so much about this organization."
Wheeler, a Type-B free agent, went 2-2 with a 4.38 ERA in 47 relief appearances in his first season with the Red Sox.
The Red Sox also declined to offer arbitration to Varitek, a Type-B free agent, last offseason but he signed a one-year, $2 million deal to play his 15th season in Boston.
Joe McDonald covers the Red Sox for ESPNBoston.com.