The Rays made a qualifying offer to Cobb, but the right-hander said Friday he wouldn't mind being reunited with manager Joe Maddon and new Cubs pitching coach Jim Hickey.
"Obviously, if we move down the line and we're able to have some discussions with them, I'd be very honored to be able to talk with them and hopefully come to a deal," Cobb said during an interview with MLB Network Radio.
Cobb, who turned 30 last month, hinted that he will most likely reject the Rays' qualifying offer.
"You're talking about, hopefully, a decision that's going to impact the next five years of your life," Cobb said.
Cubs president of baseball operations Theo Epstein and general manager Jed Hoyer will likely meet with Cobb's agent during the General Managers Meetings, which begin Monday in Orlando, Fla.
The Cubs need to fill two holes in the rotation, as both Jake Arrieta and John Lackey are free agents. Hickey, who has not been formally announced as the Cubs' pitching coach, has started reviewing video of some of the other free agents available as the team considers its options for a closer as well.
Last season, Cobb was second on the Rays in innings pitched with 179 1/3, posting a 12-10 record and 3.66 ERA in his 29 starts. He underwent Tommy John surgery on his right elbow in May 2015.
During an interview this past week with 670 The Score in Chicago, Hickey recommended Cobb.
"I would trust the arm 100 percent, especially because he did miss the time that he missed," Hickey said. "The usage is minimal for a 30-year-old type of pitcher. What he did with basically two pitches in the American League East last year was remarkable -- incredible, really."
Cobb complimented both Maddon and Hickey.
"I don't hide the fact that I have the most respect for Joe Maddon and what he did for me coming up as a player, and not so much as a pitcher on the mound, but as a professional athlete and a professional baseball player," Cobb said. "It had to do with the mental side of the game and how to deal with the stresses that come with a big league lifestyle. There's nobody better in the game to control and to deal with people as he is."
Hickey has been Cobb's pitching coach in Tampa Bay since the right-hander made his Major League debut in 2011.
"I can't say enough good things about him," Cobb said of Hickey. "He's not only a good pitching coach, but a real close friend of mine."
The Cubs have reached the postseason the past three years. That's also appealing to Cobb.
"You make a ranking system of what's most important to you and your family," Cobb said. "No. 1, first and foremost, is that we're going to a place that we feel is going to be winners for the length of the contract. I've been through losing and winning seasons. The amount of joy that winning brings can't be replaced by a dollar figure. That's our No. 1 decision-based reasoning."
Carrie Muskat has covered the Cubs since 1987, and for MLB.com since 2001. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.