The Rangers are clearly in a dire situation. They've traded off Jurickson Profar for 4 minor league players who, even though they're not top 100 prospects, seem to have shown some promise in the minors, and most of them are ranked on the Rangers top 30 list.
However, the Rangers farm is still far from good after the Profar trade. They don't have very much talent that will bring back a haul, however, it's not completely devoid of anything decent. Their most valuable piece is likely Jose Leclerc. Leclerc is only 25 years old, and reaches up into the mid-to-upper 90's with his fastball. In 57 and two thirds innings, Leclerc had an ERA of just 1.57, FIP of 1.89, and WHIP of .850, while striking out batters at a 13.3 rate. Leclerc in 2017 had a walks per 9 of 7.9, but really improved in 2018, having walked batters at a 3.7 per 9 rate. All his numbers are pretty impressive for playing in a very batter friendly park, including only giving up 1 home run. Leclerc also bring value in both his late inning experience, and the fact he's yet to reach arbitration. Whichever team loses out on Craig Kimbrel between the Red Sox and Braves could show some interest in the right hander. The Dodgers could also look into Leclerc to set-up all-star closer Kenley Jansen.
Elvis Andrus could also be on the move. Andrus is coming off a season where he missed time with injury, and batted only .256/.308/.367 and worth just 78 wRC+. However, he did bat a combined .299/.348/.457 between 2016 and 2017. Elvis is still a good defender up the middle. Last year, he had 5 DRS, 3.0 UZR, and a total 1.2 dWAR at short. Plus, he brings some value in his speed. Given a full healthy season, Andrus can provide a team with good batting numbers, 25 stolen bases, and defense up the middle. Andrus' contract does include an opt-out after the 2019 season, but I doubt he could get more than $14-$15 AAV that his contract guarantees through 2022, so unless he has a crazy season next year, he'll likely not be just a rental. However right now after coming off of a down season, the Rangers best option may be to keep Andrus for now, and trade him later in the season if he bounces back.
Another name that has received some attention in recent rumors is Mike Minor. Minor worked as a starter last season, and turned in middling results. Overall, he pitched in 157 innings, to a tune of a 4.18 ERA, 4.43 FIP, and 1.121 WHIP, while walking only 2.2 batters per 9. However Arlington is a very hitter friendly park. Plus, in the second half of the season, Minor pitched for a 2.97 ERA, 4.18 FIP, and .936 WHIP. Minor also can serve as a relief pitcher. In 2017, MM served as a setup man for the Royals. In 77 and two thirds innings, Minor had a 2.55 ERA, 2.62 FIP, and 1.017 WHIP. He only gave up 5 home runs, 22 walks, and struck out 88 batters. The Phillies have been linked to the lefty, but even though he's affordably controlled through 2020 ($9.83 million AAV), the Rangers have asked the Phillies about multiple top pitching prospects from the Phils. The Rangers will likely have to lower their price a bit before moving Minor.
Rougned Odor is a third player the Rangers could look to try to sell off. Odor is entering his age 25 season, and made some huge strides in his game last season. From 2014 to 2017, Odor's OBP was just .287, but in 2018 he raised it to .326. Plus, his defense went from sub-par to impressive in 2018. At second base, Odor recorded 11 DRS, 6.9 UZR, and 1.5 dWAR. Overall in 535 PA's, Odor batted .253/.326/.424 with a 97 wRC+. Along with solid offense, Odor can bring some power and speed to a line-up. The last 3 seasons have seen Rougned Odor have double digits in home runs and stolen bases. Between 2016 and 2017, Odor had a total of 63. Odor is controlled through 2022+a team option for $13.5 million in 2023. Next year, he is owed $9.3 million, and through 2020-2022, he is owed between $9.33-$12 million AAV.
Joey Gallo is one of the last players the Rangers have that holds value. The true three true outcomes player batted .206/.312/.498 with 40 home runs and 92 RBI's. Fangraphs also gave Gallo 11 wRC+, a .343 wOBA, and .292 ISO. Gallo brings value in his utility as well. He has experience at all 3 outfield positions, plus time at first base and third base. While he'll never win a gold glove, throughout his career, he's been worth -.6 dWAR. Like Odor, he'll be entering his age 25 season, and with control through 2022, he could be a highly sought after player, given his age, contract, and utility.
If the Rangers capitalize now and trade Leclerc, they could bring back something decent for him. A team interested in Craig Kimbrel, Zach Britton, David Robertson, and Adam Ottavino could turn to Leclerc as a cheaper option in terms of money. Then later in the season, they can trade Mike Minor and Elvis Andrus, depending on if Minor continues his late season success of 2018, and/or Andrus bounces back. Both could bring back a decent prospect pending on performance. There should be no rush on Gallo right now. Gallo's main weakness is hitting into the shift, and at his young age, there's plenty of room and time for him to learn better techniques to hit against the shift. If they're able to get decent pieces from all 5 players, we could see them re-enter contention by 2020-2021, depending on the pieces they get back.