Indians general manager Chris Antonetti said he spoke with Masterson about the talks Friday. The sides may resume negotiations at a later time.
Masterson, projected to be one of the top starters in free agency next offseason, is seeking a multiyear deal worth about $17 million annually, according to reports. The right-hander's agent proposed multiple offers to the Indians more than two weeks ago.
In spring training Friday, Masterson threw six strong innings in a 14-3 rout of the Colorado Rockies.
Masterson's spring training scoreless streak was snapped after 14 2/3 innings in the Scottsdale, Ariz., game, with both runs against him scoring on wild pitches. While he doubled his walks total to four, Masterson struck out six and allowed five hits in his next-to-last start before Opening Day.
"So even though it didn't happen right now, I'm not overly disappointed," Masterson said.
Agent Randy Rowley indicated to MLB.com that Masterson, who turns 29 on Saturday, will test the open market following the 2014 season.
"We tried to be flexible in years and sensitive to the market," Rowley told MLB.com. "Justin obviously has a passion for playing for [manager Terry Francona], loves his teammates and we would've loved to have gotten something done.
"We tried to do everything we could to make that happen, and we weren't able to come to an agreement."
Masterson has emerged as a reliable starter over the past three seasons, going 37-35 with a 3.86 ERA while averaging 205 innings pitched over that stretch. He and the Indians avoided arbitration in February with a one-year contract worth $9,726,500. He is eligible for free agency after the season.
Antonetti also would not discuss the possibility of a new deal for second baseman Jason Kipnis.
Information from The Associated Press was used in this report.