The Broncos slapped a first-round tender on Marshall, but teams were unwilling to part with a first-round draft pick as compensation to lure the restricted free agent out of Denver.
Marshall posted his third consecutive 100-catch season last year and made his second straight trip to the Pro Bowl despite several run-ins with coach Josh McDaniels.
He was suspended for insubordination in training camp and again for the season finale after he was tardy for treatment on a hamstring injury the team felt he was exaggerating.
Still, Marshall caught 101 passes last season, including an NFL-record 21 in a loss at Indianapolis. His 10 touchdowns were a career best.
A team spokesman confirmed that Marshall signed his tender on Tuesday but declined to comment further. A message was left with Marshall's agent, Kennard McGuire, seeking comment.
The Seattle Seahawks were the only team that had Marshall in for a visit during free agency, flying him in on a seaplane. The Seahawks, however, were unwilling to part with the sixth pick in the upcoming draft to sign him, although they remain interested in the physical 6-foot-4 receiver.
Seahawks coach Pete Carroll acknowledged interest after the team's first minicamp practice Tuesday.
"We've done our homework and done our research on that. Really, it's not in our hands," Carroll said. "The Broncos have some things that they have to do. We're on alert here."
For all his talents on the field, Marshall has had several run-ins with the law and visits to commissioner Roger Goodell's office to discuss his off-the-field behavior. He was suspended for the 2008 opener following a series of domestic disputes involving a former girlfriend.
In February, an emotional Marshall was a witness in the murder trial of Willie Clark, who was convicted in the 2007 drive-by slaying of Broncos cornerback Darrent Williams.
Last summer, Marshall was suspended by the team for throwing a tantrum at practice during training camp. The source of his 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 rookie deal he signed in 2006 as a fourth-round draft 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 that Denver tendered last month, including NFL sacks leader Elvis Dumervil and quarterback Kyle Orton. Marshall is the second one 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 is 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.
Orton would lose his top target if the Broncos trade Marshall. The quarterback said recently that he was working hard to develop a better rapport with third-year wideout Eddie Royal, the forgotten man in Denver's revamped offense last season.