The 35-year-old starter most likely will be traded to a contending team before the deadline for non-waiver deals on July 31. The Cubs hit the road on Friday and don't return until July 27.
Dempster enjoyed playing catch and pitching to his six-year-old son Brady for 45 minutes before Thursday's game against Miami.
"It's great to hear teams are interested, but there is nothing imminent as far as I know of," Dempster said. "I am sure if they have something they will come to me with it, so right now I am getting ready for tomorrow's game."
Because he's been in the majors at least 10 years and five with the same team, Dempster can veto any trade.
Dempster is set to pitch against St. Louis on Friday, and his next start would be in Pittsburgh on July 25 at PNC park. According to numerous major league sources, the Dodgers and Braves have been the front runners for Dempster, but late entries like the Yankees, Boston and the Cardinals have attractive young players to offer the Cubs in a deal as well.
"I understand this is part of the process and part of the business, but for me it is business as usual," Dempster said. "The guys have been really great dealing with lots of stuff and lots of rumors."
Dempster is among the hottest pitchers in baseball, riding a 33-inning scoreless streak over his last five starts.