Napoli, 31, said Monday that he's received interest from "a bunch of teams," although he didn't name them.
The latest team to join that fray is the Boston Red Sox, a source told ESPN The Magazine's Buster Olney. The Red Sox, like some other teams, might look at Napoli as someone who can play catcher or first base, or be a designated hitter. Napoli said he's willing to play those spots if it gets him in the lineup.
"I just want to play," Napoli said. "I feel the most comfortable behind the plate because that's where most of my reps have been. Do I think I can be good at first base if I had reps and practiced it all the time? Yes. But it's not like I'm saying I have to be a catcher. I just want to be in the lineup and play. If it helps at catcher, I'll catch, or at first base, I'll play there. But I like catching. I look at myself as catcher."
Napoli said he wasn't surprised the Rangers didn't make him a one-year, $13.3 million qualifying offer.
"It's a business, and that's how they felt, and I understand that," Napoli said.
That decision hasn't deterred Napoli's desire to play for manager Ron Washington and the Rangers, the team that traded for him before the 2011 season. Texas is still in need of a catcher and has expressed interest in Napoli.
"I love playing in Texas," Napoli said. "I love the atmosphere there, the clubhouse, playing for Wash, a winning ballclub. I love playing there. I know how the Rangers' clubhouse is, and it's amazing. I've never been a part of anything like that in terms of chemistry and how everyone is.
"There's been a bunch of teams that have called my agent and shown interest, and we're going to listen and see what they have to say."
Napoli said he plans to begin his workouts on Wednesday and has taken advantage of the chance to rest his body so far this offseason. Napoli missed more than a month (Aug. 11-Sept. 14) with a left quadriceps strain, and he's convinced that rest was good for that injury, too. Napoli is focused on bouncing back from a season in which he hit .227 in 108 games with 24 homers and 56 RBIs. He had 125 strikeouts, averaging 1.15 per game, the most in his career.
"Obviously, I didn't have the year I wanted to," said Napoli, who hit .320 the previous season with 30 homers and 75 RBIs and had a terrific second half in 2011. "But I feel like I'm a better average hitter than that. My career numbers show that. I had a rough year averagewise and hitting with runners in scoring position (.245), and I struck out more than past years. It was a weird year for me, mentally and physically. I battled injuries all year."
Napoli said he's not in any rush to make a decision about his new team and will let the process play itself out. "I want to play for a winning team," Napoli said.