The Rangers are reportedly engaged in ongoing trade discussions with the Rays concerning starting left-handed pitcher Matt Moore, according to MLB.com columnist Jon Paul Morosi.
The trade talks have included Rays relievers as well, Morosi reports. The Rangers are said to be in the market for a late-inning reliever and starting pitching.
In addition to Moore, trade rumors are swirling around Tampa Bay startersJake Odorizzi and Chris Archer, writes MLB.com's Bill Chastain.
The Red Sox, Orioles, Blue Jays, Yankees, Rangers, Dodgers, Pirates, Marlins, Mets and Astros are among the clubs looking for arms. It's unclear if the Rays would consider a trade with a division rival.
Here is a look at some other rumors circulating ahead of the Aug. 1 non-waiver Trade Deadline:
Yankees could move Chapman, Beltran
Are the Yankees buyers or sellers? That's been one of the biggest questions leading into the Trade Deadline.
A report Saturday from MLB Network insider Ken Rosenthal suggests the Yankees would be willing to trade pending free agents Aroldis Chapman and Carlos Beltrán if the club is not in serious contention for a postseason berth by Aug. 1.
The Yankees have lost two straight to open the second-half and are in fourth place in the American League East, 9 1/2 games behind the division-leading Orioles. New York is 5 1/2 games out of the second AL Wild Card spot.
Beltran has a limited no-trade clause, but the Yankees will still field offers for the veteran outfielder and left-handed closer Chapman if they fall out of the playoff race, according to Rosenthal. The Yankees reportedly do not want to trade lefty reliever Andrew Miller.

Buchholz prepared for possible trade
Clay Buchholz realizes his time with the Red Sox could soon come to an end with the non-waiver Trade Deadline looming, reports MLB.com's Ian Browne. Buchholz is currently in the bullpen and a crowded Boston rotation recently added Drew Pomeranz. In a pitching-thin market, Buchholz could attract interest from a number of clubs.
"The way I've always looked at it is this team is run as a business," said Buchholz. "They're going to do everything they can if it's going to make them better, and if that involves moving me somewhere, that's what it is. I don't have any control over that."
Buchholz is 2-8 with a 6.31 ERA as a starter this season, and he twice has been bounced from the rotation. Buchholz is earning $13 million this season and has a $13.5 million club option for next year ($500,000 buyout).

Dodgers among teams scouting Archer
The Dodgers were among the clubs scouting Rays pitcher Chris Archer during his start Friday night, reports MLB.com's Ken Gurnick. Dodgers president of baseball operations Andrew Friedman knows Archer well, having acquired the right-hander in 2011 when he ran the Rays.
Archer, 27, is 4-13 with a 4.68 ERA this season. He is signed through 2021.

Marlins surveying pitching market
The Marlins are looking to upgrade their rotation and are open to all possibilities, though the club would be hesitant to deal players off its active roster, reports MLB.com's Joe Frisaro.
The Marlins have been linked to starters such as A's left-hander Rich Hill and Yankees right-handers Michael Pineda and Nathan Eovaldi. Hill is a free agent after the season.
Rosenthal reported Miami could be open to trading shortstop Adeiny Hechavarria to the Rays for Archer. However, such a deal would appear difficult to pull off, Frisaro writes.
"As we look at this club, we'll continue to look at ways to upgrade the roster and help us win more games," Marlins president of baseball operations Michael Hill said.

Mets in market for bullpen arms
The Mets are looking to add an experienced right-handed pitcher to their bullpen, according to a report from Newsday citing unnamed sources.
New York relievers entered Saturday with 3.20 ERA, good for third in the National League and sixth in the Majors.
The Mets reportedly were close to signing Kevin Jepsen after he was released by the Twins, and he ended up with the Rays. The Mets are also said to be skeptical of the cost benefits of top-line relievers like Milwaukee's Jeremy Jeffress.
Upton drawing interest
Padres outfielder Melvin Upton Jr. is "opening eyes" and drawing trade interest, San Diego general manager A.J. Preller tells USA Today.
Upton, 31, is hitting .262 with 16 home runs and 20 stolen bases through 87 games. He's robbed three home runs in the outfield and hit a walk-off homer of his own as arguably the most electric player for the Padres this year. Upton is earning $15.45 million this year and is owed $16.45 million next season.