A Broncos spokesman confirmed to The Associated Press that Marshall signed his tender, but declined to comment further. AP also left a message with Marshall's agent, Kennard McGuire, seeking comment.
"We've done our homework and done our research on that," Carroll said. "Really, it's not in our hands. The Broncos have some things that they have to do. We're on alert here."
Marshall posted his third consecutive 100-catch season last year and made his second consecutive trip to the Pro Bowl despite several run-ins with Broncos coach Josh McDaniels. Marshall had an NFL-record 21 receptions during a Dec. 13 loss at Indianapolis, and his 10 touchdowns for the season were a career best.
But for all his talents on the field, Marshall has had several run-ins with the law and visits to NFL Commissioner Roger Goodell's office to discuss off-the-field behavior. Marshall was suspended for the 2008 season opener following a series of domestic disputes involving a former girlfriend.
Last summer, the Broncos suspended Marshall for throwing a tantrum during a training-camp practice. The source of Marshall's frustration was twofold: He was upset with the team's medical staff for misdiagnosing a hip injury that required offseason surgery, and he was displeased with his contract.
Marshall earned $2.2 million last season in the final year of the deal that he signed in 2006 as a fourth-round pick out of Central Florida. He wants to be compensated like other elite wide receivers in the NFL, which would mean a pay hike of $6 million to $8 million annually.
Marshall was one of five restricted free agents whom the Broncos tendered last month, including NFL sacks leader Elvis Dumervil and starting quarterback Kyle Orton. Marshall is the second player to sign his tender, although offensive lineman Chris Kuper's signing wasn't viewed as a means to a trade.
Orton hasn't signed his tender, but he's participating in the Broncos' offseason training program, something Marshall, Dumervil and tight end Tony Scheffler, another restricted free agent hoping for a ticket out of Denver, have been skipping.
The Associated Press contributed to this report.