Scouts have been following Samardzija closely this season, and the Blue Jays had two representatives in Miami on Tuesday night for his last start.
Samardzija is the only pitcher in baseball to make at least 12 starts this year and only have two wins despite a sub-3.00 ERA. Is he immune to the speculation and rumors?
"Numb would be a good word," Samardzija said Tuesday. "I'm just out doing my job. I feel good. I'm really excited, compared to these last two years of starting. I feel really good where I'm at with my routine and my arm feels great. ... I'm going to keep doing my job and I'm not too worried about that stuff -- it'll take care of itself."
Samardzija has one more year of arbitration left and will be a free agent after the 2015 season. He told his agent he did not want to be distracted by contract talk until something had been finalized.
Neither Samardzija's agent nor Cubs president of baseball operations Theo Epstein would comment on the report or their discussions.
According to reports, Samardzija is rumored to be looking for a contract in the $100 million-plus range, which is where starting pitchers such as St. Louis' Adam Wainwright ($97.5 million) and Cincinnati's Homer Bailey ($105 million) sit.
This is Samardzija's third season as a full-time starter, and it's his best, despite a 2-6 record. He would appear to be the type of pitcher the Cubs want to move forward with in their rotation, but Epstein has been intent on rebuilding the farm system and has traded two starting pitchers each of the past two seasons, including Matt Garza and Scott Feldman last year. Jason Hammel and Jake Arrieta also have reportedly drawn interest from teams looking for starting pitching.
"We have a couple guys on the trading block, but that's what comes with being quality starters or being able to pitch at the level some of the guys can," said Arrieta after beating the Marlins on Wednesday in Miami. "I look forward to having Jason and Jeff as teammates as long as possible. Obviously, I'd like them both to stay here. Theo and Jed [Hoyer, general manager] will do everything in their power to put the best team on the field, whether it's keeping those guys or swapping them for prospects who they feel can be here for a long time.
"It's really not something we need to think about. You have to continue to go day to day and see what happens. I'd love to see those guys stick around."
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. Alex Smith is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.