The Rockies, who train in Arizona, added that there will be no further discussions.
Earlier in the day, as talks were ongoing, Monfort said there would be no bargain-basement deal.
"This is Todd Helton we're talking about," he told The Associated Press. "We're not just going to give him up for nothing."
Red Sox spokesman John Blake told MLB.com on Monday night that the Red Sox would have no official comment, but added that Monfort's statement spoke for both parties.
Helton is a career .333 hitter, with a .596 slugging percentage, over nine Major League seasons, and is four RBIs shy of 1,000.
The Red Sox were said to be offering third baseman Mike Lowell (one year, $9 million remaining) and right-hander Julian Tavarez in exchange for Helton. The Rockies were interested in young pitching, with various reports pointing toward Craig Hansen and Manny Delcarmen as possible chips in any deal.
Helton told The Denver Post over the weekend that he would waive his no-trade clause to play in Boston, but also indicated that he wants a deal to happen quickly or else he wouldn't approve one.
In the end, there were two key sticking points. First, the two sides could not come to an agreement on how to split the remaining $90.1 million left on Helton's contract. Sources told The Boston Globe that the Rockies may have been willing to absorb up to half the remaining value on Helton's contract, which runs through 2011, with an option for 2012.
The second stumbling block was which prospects would have headed to Colorado as part of any package. The Rockies were said to be asking for young pitching, with Hansen, Delcarmen, Clay Buchholz and Jon Lester rumored to be discussed.
The Boston Herald reported on Monday that Josh Beckett, while watching the movie "Fever Pitch" over the weekend at his Florida home, had thrown his support behind the left-handed-hitting slugger. On Monday, another Sox pitcher, Curt Schilling, called Helton "the toughest out, by far" he's ever faced in the Majors. Schilling made his comments to WEEI-AM in Boston while announcing that he would not retire after this season and would pitch again in 2008.