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Monson's representation told ESPN.com that Minnesota will pay Monson $1,100,590 and then will pay him for four months of salary through March 2007 for an estimated total of $1.35 million.
ESPN.com's Andy Katz reported that Monson was told earlier this week he was likely going to be out, and either he could be fired or he could resign in an attempt to get a better financial settlement.
The Minneapolis Star-Tribune's Sid Hartman was the first to report Thursday that Monson was out as head coach after taking over the scandal-ridden program in 1999.
Wednesday night's 90-68 loss to Clemson in the ACC/Big Ten Challenge may have been inconsequential after sources said Thursday that Maturi told Monson that either he had to go or there would be pressure they both may be out.
The naming of Molinari, a former Bradley head coach, as the successor was a bit of a surprise considering that Bill Walker had been the assistant at Minnesota since 1999.
Minnesota's 2-5 start includes going winless at the Old Spice Classic in Orlando with losses to Marist and Montana. The Gophers play Arizona State on Saturday.
Monson was the hot young head coach in 1999 when he led Gonzaga to the Elite Eight, which started the Zags' run to college basketball's elite. The Zags beat Minnesota in the NCAA Tournament that year in Seattle in what would be Clem Haskins' last run with the Gophers. An academic scandal hit the program and Monson was brought in to clean it up, which he did. But the Gophers struggled to keep elite players with Rick Rickert, Joel Przybilla and Kris Humphries all leaving early for the NBA draft. Monson took the Gophers to four NITs and one NCAA Tournament, in 2005.
In the preseason, he said the team had its best foundation in his eight seasons in the Twin Cities, with a freshman class including Bryce Webster and Lawrence Westbrook and redshirt freshmen Damian Johnson and Kevin Payton. But the Gophers, without a single senior, haven't won a game since beating North Dakota State and Long Island to start the season.
"I feel like I did what I was asked to come here to do," Monson said. "With that, I have no apologies for where the program is."
But he added: "It's time for somebody else to make the next step and that's to have more success on the court than I had."
Information from The Associated Press and ESPN.com's Andy Katz was used in this report.