Formerly with the Pirates, Jones signed a two-year, $7.75 million contract with Miami, leaving Morrison as a coveted trade chip.
"He's a good player, so, yes, there has been interest," president of baseball operations Michael Hill said. "We'll continue to see if there is a deal out there that makes sense."
Hill did not get into specifics regarding any possible deal for Morrison. At least 10 teams are believed to have expressed some interest. The list includes the Brewers, Rays, Pirates, Orioles and Blue Jays.
With so many scenarios out there, the Marlins are taking a wait-and-see approach. Although it is inevitable Morrison will be dealt, there is no urgency to do so before the Winter Meetings wrap up on Thursday at the Walt Disney World Swan & Dolphin Resort.
"It could happen, but we don't have to make a deal," Hill said. "We don't have to make a deal unless it makes sense for us to do it."
Morrison, 26, is arbitration-eligible for the first time, and technically, Miami has three more seasons of control for the left-handed-hitting first baseman.
Theoretically, the Marlins could stand pat with Morrison, but in reality, it's obvious he will be dealt, if not by Thursday, then sometime thereafter. Morrison is projected to make about $1.7 million in arbitration.
The Marlins are in the market for a third baseman and veteran relief pitching. If possible, the organization would like to retain its pitching depth, and not use it in trades.
Morrison becomes the club's most coveted trade piece. If he can be part of a package to fill a need, then the club will be able to retain its young arms.
Since last Friday, when it was known Jones would be joining the Marlins, a handful of teams have inquired about Morrison. The list keeps growing, and the offers have improved.
Morrison has consumed a tremendous amount of the team's attention the past two days. But Hill added, the player personnel department is capable of multi-tasking. So they continue to inquire about third-base options, as well as veteran relievers.
"If it is something that makes sense, and it helps our ballclub, then it's obviously something we'll look at and discuss as a group," Hill said. "Discussions have been active. Several teams have been involved."
While Morrison is in play, the face of the Marlins' franchise is not. Giancarlo Stanton, Miami's 24-year-old slugger, is not drawing any trade interest, mainly because the team previously has stated he is not available.
Also entering his first season of arbitration, Stanton is projected to make about $7 million next season.
All offseason, the Marlins have said publicly Stanton would be back in Miami. High-ranking club officials said so publicly last month before the General Managers Meetings in Orlando. Since word got out, opposing teams apparently have listened.
"No one has called us about Stanton," Hill said. "We wanted to put that out there."