Byrd has been on the disabled list since suffering a severe beaning on May 21 in Boston, which left him with multiple facial fractures on the left side of his face and blurred vision in his left eye.
"I'm going with the team to Kansas City over the weekend, and I'll come back on Monday and go to Iowa," Byrd told ESPNChicago.com. "I'll get my work in, and hopefully get back with the team and ready to play the following Monday."
That timeline would have him back with the Cubs on July 4, during a road trip against the Washington Nationals.
"That's the plan," Byrd said. "I hope to come back with the team on the Fourth of July and meet them in D.C."
Byrd said he wanted to begin his rehab at Triple-A in order to get as major-league ready as possible before his return.
"I'm ready to get up there and I'm anxious to see how I react when a ball is thrown very close to me," Byrd said. "I want to see if I jump away or not. I want to see if I just barely move like I always do and let the ball come close to me. As a player, I have that aggressiveness. I have that style of play. But I'm interested to see how I react to a slider that starts at my hips or a cut fastball that starts in and up."
Byrd was hitting .308 in 44 games with three homers and 11 RBIs before the injury. The 33-year-old outfielder is in the second year of a three-year contract that he signed before the 2010 season.
Bruce Levine covers the Cubs for ESPNChicago.com and ESPN 1000.