"We're still having additional conversations," general manager Jon Daniels said. "We'll see where they go but [pitching] is still our focus."
The Rangers could also address other areas of the club, as they have been linked to Brewers catcher Jonathan Lucroy.
"I wouldn't rule anything out," Daniels said. "But pitching is our priority."
Harrell is expected to replace Nick Martinez in the rotation and start on Sunday against the Royals, although the Rangers want to see him throw his bullpen session on Friday.
Alvarez is expected to be in the bullpen, giving the Rangers another left-handed option to go with Jake Diekman and Alex Claudio. Both players are expected to be added to the 25-man roster when they arrive on Thursday or Friday.
"You look at both pitchers we acquired, they can help our ballclub, fill a role and add depth," Daniels said. "With Lucas, he is a guy who is throwing the ball well. He has been around a little bit, had some experience and he has been on a little bit of a roll."
Harrell has made five starts for the Braves and was 2-2 with a 3.38 ERA and a 1.26 WHIP. Prior to that, he was 5-2 with a 3.06 ERA in 11 starts and four relief appearances at Triple-A.
He pitched in Korea in 2015, going 10-11 with a 4.93 ERA in 30 starts and three relief appearances for the LG Twins.
"I think the biggest thing for me was, last year, going to Korea," Harrell said. "There's a big language barrier, so you really have to focus on yourself and learn about what you were doing wrong. So, I had a lot of time to work with myself over there and get a feel for what I needed to do to get better.
"The Rangers have a good organization, and I played against them for several years with the Astros. They've won a lot lately, so it's going to be great to go there and try to make a postseason push."
His best year in the big leagues was in 2012 with the Astros, when he was 11-11 with a 3.76 ERA and a 1.36 WHIP over 32 starts. His pitching coach that season was Doug Brocail, now with the Rangers. Harrell was 6-17 with a 5.86 ERA in 22 starts and 14 relief appearances for the Astros in 2013, pitching on a team that lost 111 games.
"I've seen him in the past, when he was in Houston," Rangers manager Jeff Banister said. "We haven't seen him this year. I know what our scouts have been talking about, this is a guy who's been throwing the ball very well. Fastball is 92-93 mph, secondary stuff is put-in-play type of stuff. He does have some strikeouts, but he seems to have the strike ability with all his pitches."
Alvarez could be a big acquisition for the Rangers if he can continue the success he has shown briefly with the Braves. It reflects what he did in the Minor Leagues as well. Basically, he is a power left-hander with a 93-mph fastball who can get swings and misses with his slider.
"Dario is a really interesting guy," Daniels said. "For a number of years in the Minors, he had a lot of success and a lot of strikeouts. With Alvararez, obviously it's a limited sample size, but if he keeps it up, you would have to stack several Travis Demeritte on top of each other to get him."
Alvarez has pitched in 16 games for the Braves. He has struck out 28 and walked five in 15 innings with a 3.00 ERA and a 1.07 WHIP. Left-handers are hitting .217 off him, and right-handers are hitting .188. The Braves acquired him off waivers from the Mets on May 25, but over seven Minor League seasons, he has a 2.97 ERA and averaged 11.1 strikeouts per nine innings.
"This guy just kind of burst on the scene here," Braves manager Brian Snitker said. "Nobody really knew who he was. He kind of reinvented himself, and he's done enough that if I was a team sitting up there watching him, I'd want him, too, because he's a very effective left-handed pitcher right now. We hate to see him go. He's really added a lot to our bullpen."
Demeritte has batted .272 with 25 home runs and 59 RBIs over 88 games with Class A Advanced High Desert this season. He was selected by the Rangers in the first round (30th overall) of the 2013 Draft and recently played in the SiriusXM All-Star Futures Game.
The Rangers made room on the 40-man roster when Triple-A infielder Matt Duffy was designated for assignment.