Miami has been active in discussions but has yet to make a move. Dan Straily is scheduled to start on Tuesday against the Braves, but even that isn't completely certain. Straily has been scouted by a couple of clubs, including the A's, and possibly could be dealt by the Deadline.
Closer Kyle Barraclough and relievers Adam Conley, Drew Steckenrider and Brad Ziegler have been on the radar of several teams.
The biggest potential blockbuster is if All-Star catcher J.T. Realmuto is dealt. The Marlins and Nationals have had talks since the middle of last week. The asking price is extremely high, with the Marlins coveting Washington's top two prospects -- outfielder Victor Robles and shortstop Carter Kieboom - to be part of a trade package.
Indications are there hasn't been much momentum in the talks, and it is appearing more likely that Realmuto stays in Miami. However, that still could change, depending on whether the Nationals are willing to meet the Marlins' demands.
Position players like second baseman Starlin Castro, outfielder Derek Dietrich, first baseman Justin Bour, outfielder Cameron Maybin and third baseman Martin Prado also could be dealt if a trade makes sense.
"Guys are probably disappointed if their name is not in [rumors], in some way, shape or form," Marlins manager Don Mattingly said.
Castro, who is under contract through next year, said he isn't closely following trade speculation. He did note he enjoys Miami, and he sees a young team that's improving.
"I like it here," Castro said. "A lot of good guys. A lot of good players. A lot of guys who really want to play, really want to fight, really want to win. It's really fun to see."
Trade rumors are part of the profession, and talks tend to increase after the All-Star break.
"As soon as the break is over, you know it's going to be there on the tip of everybody's tongue," Mattingly said. "And there are going to be guys on our club that are going to be mentioned."
Ziegler, 38, is a free agent after the season, and the right-hander is viewed as the player most likely to be dealt.
The Cubs, Indians and Red Sox have shown consistent interest. But Cleveland added bullpen depth on Monday.
Barraclough and Conley will be arbitration eligible next year, and Steckenrider is a rookie. So, the Marlins have set a high price for their relievers' controllable years.
"Keep taking care of your business," Mattingly said of the message to the players. "Guys deal with stuff with their families. They deal with a tough loss. They deal with so much. When they get on the field, I think they're pretty good at separating the two."
Worth noting • Sandy Alcantara (right axillary infection) will throw a bullpen session on Tuesday, and then the organization will decide if he will make another rehab assignment start or rejoin the Marlins.
• Tayron Guerrero (left lumbar strain) had travel issues, so the right-hander is not throwing his scheduled inning of relief for Triple-A New Orleans on Monday. Instead, Guerrero will pitch a rehab assignment inning with Class A Advanced Jupiter on Tuesday.