Cameron, who turns 37 in January, was close to agreeing to a two-year, $15.5 million contract with the Boston Red Sox on Monday. He is projected to move to left field.
Byrd, 32, could fill Piniella's wish list of a center fielder who can drive in runs. He knocked in a career-high 89 last season and batted .295 over the past three seasons with Texas. All three of those years were under the tutelage of new Cubs hitting coach, Rudy Jaramillo.
As long as Milton Bradley is on the Cubs' payroll, however, it's tough for the team to add anyone.
The Cubs are still talking to the Tampa Bay Rays about a Bradley-for-Pat Burrell swap. And the holdup is the same: the portion of the $12 million owed Bradley in 2011 the Cubs are willing to pick up. Both Bradley and Burrell will make $9 million in 2010.
Byrd, who earned $3.06 million last season and is represented by Seth Levinson, is drawing interest from other teams, and some reports have listed the Braves, Angels, Yankees, Mariners, Mets and Giants as possible suitors.
Other center fielders on the free-agent market whom the Cubs are looking at include Rick Ankiel and Scott Podsednik. Ankiel, 30, a converted pitcher, has seen his average drop each of the past three seasons, from .285 in 2007 to .264 in '08 to .231 this year. In 122 games with the Cardinals, the left-handed hitter hit 11 homers and drove in 38 runs. In '08, he hit 25 homers and had 71 RBIs.
Podsednik, 33, rebounded this past season in his return to the White Sox, batting .304 with 30 stolen bases.
There also is a chance the Cubs could bring back Reed Johnson, who was not offered arbitration and is a free agent. Johnson, who turned 33 this month, is coming off an injury-filled season in which he was limited to 65 games.
The Cubs like Johnson, especially his defensive play, but didn't want to give him a significant raise from the $3 million he was paid last season.
Carrie Muskat is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.