ARLINGTON -- The Rangers were able to reach an agreement with four of their potential seven arbitration cases on Tuesday. They still have more work to on the other three, including closing a $3.2 million gap with catcher Mike Napoli.

On a day in which the Rangers reached agreements with outfielder David Murphy and pitchers Matt Harrison, Mark Lowe and Mike Adams, they also exchanged numbers with the three other arbitration-eligible players.

Napoli is asking for $11.5 million while the Rangers are offering $8.3 million. Napoli, who is eligible for free agency after this season, is coming off his best year in the big leagues. After being acquired from the Blue Jays, he batted .320 with 30 home runs and 75 RBIs in 113 games and 369 at-bats.

Outfielder Nelson Cruz is asking for $7.5 million while the Rangers are offering $5.5 million. Shortstop Elvis Andrus is asking for $3.6 million while the Rangers are offering $2.65 million.

"We had seven guys eligible going into the process," assistant general manager Thad Levine said. "We're always hopeful and optimistic about getting them done before coming to the conclusion of the process. The goal was to get them all done [Tuesday], so that's slightly disappointing. We're still glad to get a negotiated agreement with four and hopefully we can get a settled agreement with the other three."

The two sides have at least a couple weeks to reach an agreement. If they fail to do so, an arbitration hearing will be held in front of a three-person panel at some point in February. Both sides will present their case and the panel must rule for either the player or the club. The Rangers have not had an arbitration hearing since Lee Stevens in 2000.

"Anytime you file you are one step closer to a hearing," Levine said. "All parties are aware that is a possible outcome. We have historically found ways to avoid a hearing. At some point we will go, but it will only be after exploring all avenues to avoid one."

While Napoli can be a free agent after this coming season, Cruz still has two years to go and Andrus isn't eligible until after 2014. Last year the Rangers avoided two years of arbitration with Josh Hamilton with a two-year contract. Like Napoli, he can still be a free agent after this coming season.

"It's our responsibility to understand and explore all alternatives before going to a hearing," Levine said.

Harrison exchanged numbers with the Rangers and was asking for $3.5 million while the Rangers were offering $2.45 million. They settled at $2.95 million.

Lowe's deal is worth $1.7 million, Adams' is worth $4.4 million and Murphy's is worth $3,625,000 plus incentives. Murphy is not a free agent until after the 2013 season.

Lowe, who will be a free agent after this season, appeared in 52 games out of the bullpen for Texas in 2011, posting a 3.80 ERA and a 2-3 record.

He spent all but two weeks of the season with the big league club and was third on the team in appearances, while also recording 42 strikeouts in 45 innings. The right-hander allowed just six of 32 inherited runners (18.8 percent) to score, which was ninth best among American League relievers.

Murphy appeared in 120 games as the club's fourth outfielder, and hit .275 with 11 homers and 46 RBIs in 404 at-bats.

He was drafted by the Red Sox in the first round of the 2003 First-Year Player Draft and has spent his six big league seasons in Boston (2006-07) and Texas (2007-2011). Murphy has driven in at least 46 runs and hit at least 11 homers in each of his last four seasons.

Adams, who was acquired by the Rangers from the Padres at the non-waiver Trade Deadline last season, went a combined 5-4 with a 1.47 ERA through 73 2/3 innings in 2011.

The right-hander has posted an ERA under 1.76 in each of the last three seasons, pitching at least 37 innings in each of them. He also can be a free agent after this season.