"My agent is talking to the team, but I don't know how far he's going right now," Castro said. "I want to, but I don't pay attention about that. [I'm] letting my agent work and let's see how far it goes."
CSNChicago.com was first to report on the club's conversations with the two-time All-Star. Kinzer told the website that "Starlin loves being a Chicago Cub and would like to play there his entire career. ... We have been talking about a long-term deal."
Castro cannot become a free agent until after the 2016 season. The Cubs would be buying out his remaining arbitration years and at least two years of free agency, should the extension be for six or more years, as CSNChicago.com reported.
In his third season with Chicago, the 22-year-old is batting .276 with 12 home runs, 58 RBIs and 19 stolen bases. He led the National League with 207 hits last season, when he batted .307.
"I want to be here, I want to be with the team for a long time," Castro said. "I want to be on this team my whole career. I don't want to go nowhere. I want to finish my career here. That's why I tell my agent I want to be here. I want to help the team."
The native of the Dominican Republic signed with the Cubs as an amateur free agent in 2006.
"I don't want to put more pressure on myself," Castro said. "I'm letting my agent work, and I said, 'You tell me when you're close. When you're close and you're ready to go, you tell me.' But for right now, it's key to keep more concentration to the game."
Mark Clements is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.