The club also opted to make a qualifying offer of $13.3 million (average salary of top 125 players) to Josh Hamilton, guaranteeing the Rangers draft-pick compensation should the free agent sign with another team.
The Rangers were not willing to offer that same figure to Napoli, and will get nothing if he signs with another team.
"We'd like to have Nap back, but at the predetermined figure we weren't comfortable there," Texas general manager Jon Daniels said. "We're going to continue to talk and the door's very much open."
Friday was the deadline to submit qualifying offers to teams' free agents, and Hamilton was the lone one to which the Rangers made an offer. Hamilton has until 4 p.m. on Nov. 9 to make a decision. He's made it clear he plans to test the free agent market, making the rejection of the offer a formality.
Daniels said it was a difficult decision to make on Napoli, who has been the team's primary catcher the last two seasons. He made $9.4 million this season, and the club wasn't comfortable with its first investment toward next year being more than $13 million for a catcher who hit .227 in 2011. There also were no guarantees Napoli would accept the offer.
"He's going to want to test the waters, test the market. He's already done that this week, I'm sure," Daniels said. "Once we get past tonight, you're going to get a clearer picture at what team's interests are. They're looking at their options and we are as well."
Without Napoli the Rangers are thin at catcher. Geovany Soto -- who the Rangers acquired at the trade deadline last year -- is the best option on the roster, but he hit just .196 after coming to Texas. He also made $4.3 million this season and is arbitration eligible, so the club might not want to tender a contract to him before arbitration.
The only other catchers on the 40-man roster are Luis Martinez and Konrad Schmidt.
"It's not a good year to need catching," Daniels said. "We're aware of that. We're going to look at all our options, free agent and trade."
While the Rangers actively will pursue a catcher, the Ogando move takes some of the emphasis off finding a starter.
Ogando was an All-Star starter in 2010, but spent the majority of the 2011 season in the bullpen. But Texas has just three starters on its current roster who will be healthy enough to start Opening Day – Yu Darvish, Derek Holland and Matt Harrison.
Ogando gives them another solid candidate. He won 13 games in 2010 but was back in the bullpen for 57 of his 58 appearances.
The Rangers made a similar move with Neftali Feliz following the 2010 season.
"He earned that a year ago and then some of the moves we made with Joe (Nathan) and how that affected Neftali and with Darvish, Alexi agreed to go back to the bullpen," Daniels said. "I thought he handled that extremely well, team first. This guy's an All-Star starter in essentially his rookie debut in that role. He's a strike thrower and he wants to do that."
In addition to Napoli, the club did not make offers to pitchers Mike Adams, Scott Feldman, Mark Lowe, Yoshinori Tateyama and Koji Uehara.