Adam Schefter, who will join ESPN in August, reported Monday on KOA in Denver that Marshall requested the trade during a meeting Friday.
Marshall's agent, Kennard McGuire, confirmed that to ESPN's Michael Smith on Tuesday: "There was a meeting with Mr. Bowlen and Brandon did ask to be traded. He was told by ownership that the team would do everything in its power to accommodate those wishes. We do feel that a change of scenery is not only important but necessary."
According to a source, Smith reported, Marshall has met with Bowlen more than once in the past week and on both occasions expressed his desire to be dealt.
McGuire had no comment on the number of meetings that took place.
Marshall posted a message Tuesday on his blog, www.bmarshall15.com/blog, making it explicitly clear he expects to be somewhere other than Denver before the season starts.
"To whom it may concern. Life is filled with change, and where I am in my life now change is probably best. It's hard leaving an organization ran by one of the best owners in all of sports, and someone who's been there for me through my ups and downs. The hardest thing was hearing Mr. B wish me luck in the future, but we both came to the conclusion that this is probably the best thing for me to grow on and off the field.
"I thank the Denver fans who embraced my emotion and play on the field and showing me love every time I step outside my door."
Broncos coach Josh McDaniels would not say whether Marshall requested a trade, but he told ESPN's Ed Werder on Tuesday that internal meetings conducted after the holdout receiver's discussions with Bowlen suggest Denver plans to keep the player.
"We met after Pat's meeting with Brandon Marshall, and we've decided that we will continue to have a dialogue with Brandon and his representative, but we are looking forward to having Brandon at training camp," McDaniels said to Werder.
Marshall skipped Denver's mandatory minicamp Friday through Sunday. He is protesting because he has medical trust issues and he also wants a pay raise. Marshall's contract expires after next season.
The receiver had hip surgery in March and won't be able to practice until training camp starts late next month. Still, he was required to rehabilitate at the facility during minicamp. Denver can fine him for missing the sessions.
Marshall is entering his fourth season and made his first Pro Bowl in 2008. He has had back-to-back 100-plus catch seasons.
The Marshall situation is another issue for McDaniels. The former New England offensive coordinator took over in the offseason for Mike Shanahan, who was fired after 14 years with the Broncos.
McDaniels' tenure in Denver got off to a rocky start when Pro Bowl quarterback Jay Cutler was traded to Chicago. The saga began when Cutler caught wind that the new coach was considering trading him in a package for Matt Cassel, who starred for McDaniels in New England last season.
Bill Williamson covers the AFC West for ESPN.com. Michael Smith and Ed Werder are reporters for ESPN.