But the Rangers are also seriously considering left-hander John Danks and right-hander Thomas Diamond, two former No. 1 draft picks who were sent to the Minor Leagues earlier this month.
That would be a gamble, considering they have yet to pitch above Double-A. But the Rangers weren't too enamored with what they saw with Volquez and Dominguez at the end of spring.
"We're hoping for the best and preparing for everything else," Rangers general manager Jon Daniels said. "We're going to look at our internal options and keep our external conversations going."
This is almost the same injury that tormented Eaton last summer, forcing him to miss more than two months with two different trips to the disabled list.
"Pretty much one pitch, the last pitch I threw," Eaton said. "Similar injury, different tendon. It feels the same, just a different part."
Last year's injury was to a tendon in the middle of the finger. This pain is more toward the base but Eaton didn't like his chances of avoiding an extended stay on the disabled list.
"I can feel the finger, and slim [chance] it is on it's way out," Eaton said.
Eaton, acquired from San Diego in the offseason, faced just nine batters before feeling the tendon bite him on one curveball to Padres outfielder Dave Roberts. Trainer Jamie Reed and Showalter went to the mound and Eaton immediately left the game.
Asked what his first thoughts were, Eaton said, "Three weeks ... no throwing."
Eaton was supposed to start on Tuesday against the Detroit Tigers but said, "Judging by last year, I'm going to miss more than one start. It hurts just to squeeze the ball. I knew I couldn't put any pressure on it to throw a breaking ball."
Eaton, at the time off to the best start of his career, injured the finger on June 15 last year against the Detroit Tigers and went on the disabled list the next day.
He was activated on Aug. 1, allowing four runs in two innings in two relief appearances before going back on the disabled list on Aug. 9. He wasn't activated until Aug. 26.
"We did everything we could to speed up the process last year, but the only thing you can really do is rest it," said Eaton, who makes $4.65 million this season and can be a free agent afterward.
The injury ruined his season. He was 9-2 with a 3.42 ERA before the injury occurred and 2-3 with a 5.74 ERA after he hurt the finger.
"This was a big year for him," Padres pitcher Jake Peavy said. "I never pull against people, but you always pull for your buddies. I'm one of his biggest fans. I grew up in the game with the guy and I hate it he's going to miss time."
Eaton passed a physical with the Rangers before the trade was completed.
"It's always a game of adjustments," Showalter said. "We make the mistake of looking at the end of spring with finality. You have to make adjustments. The organization has done a good job of adding depth to our pitching and we're going to attack that."
Daniels has had some conversations with other general managers about pitching but said there is nothing close. The Rangers have had no further contact with Roger Clemens or his agents about when he might pitch again.
"They've made it clear and Roger has made it clear that there's a timeline to the decision," Daniels said.
Brian Anderson, recovering from Tommy John elbow surgery, is not expected to be back until June 1, at the earliest.
Right now the replacement will come from within the organization, and Danks and Diamond will get strong consideration.