But on Wednesday, D-backs president Derrick Hall downplayed that report, along with others that have surfaced since Tuesday.
"I think it's just that: It's a lot of rumors," Hall told ABC15's Jason Snavely at the 2018 Waste Management Phoenix Open Tee-Off Luncheon in Scottsdale on Wednesday. "I think any time you have Zack Greinke on your roster, teams are going to ask about him and if he's available, and I think that's more of what has happened, so word gets out.
"We'll meet with the other 29 teams as we have and go over every player on every roster. So, I think it slips out that you're asked about a player or you talk about a player, so they assume a deal is going to get done, and that's not the case here."
According to Sullivan, the D-backs and Rangers have engaged in preliminary talks about Greinke, who was instrumental in leading the D-backs to a 2017 playoff appearance. "A lot must happen for the Rangers to get Greinke but the discussions with the D-backs are real and ongoing," he said.
On Wednesday, FOX Sports' Ken Rosenthal and MLB Network's Jon Heyman backed Sullivan's report.
Rosenthal said discussions between the D-backs and Rangers are "real but complex on several fronts." He added other teams have also reached out to the D-backs about Greinke, who is still owed $127 million in the four remaining years of his contract.
Sources: Talk between #Rangers and #DBacks on Greinke is real but complex on several fronts. Other clubs also inquiring on Greinke. AZ would need to have another SP in place if it moves Greinke (or Corbin). Question of whether #DBacks would take Choo, play him in LF vs. RHPs.
Heyman reported the D-backs want to shed Greinke's salary in order to possible retain slugger J.D. Martinez, whom the D-backs acquired from the Detroit Tigers before the 2017 trade deadline. Martinez is a free agent who has become a top target of several teams.
Heyman reported Martinez is scheduled to meet with the D-backs and Red Sox on Wednesday.
GMs would be shocked if d-backs could unload greinke contract without offsetting much of it. Mike Hazen deserves to repeat as exec of year if he does.
Heyman believes the Rangers are more interested in adding mid-rotation depth than in acquiring a top-tier pitcher like Greinke. But Heyman confirmed Rosenthal's report that multiple teams are interested in Greinke's services.
The 34-year-old Greinke was signed to a six-year, $206.5 million contract by the Diamondbacks before the 2016 season. Greinke struggled in his first year in Arizona but posted a 3.20 ERA with 215 strikeouts last season. He was a 2017 All-Star Game selection and finished fourth in National League Cy Young voting.
"We wouldn't have been where we are last year without him," Hall told Snavely. "He was truly our ace, and he's so talented. It's no surprise to us that teams ask about him, as they should."
Greinke has played in 14 MLB seasons and has a career 3.40 ERA. He won the 2009 American League Cy Young award as a member of the Kansas City Royals. He has also played for the Milwaukee Brewers and Los Angeles Dodgers.