Cordero is at his home in the Dominican Republic and isn't expected to come to Cincinnati until Tuesday or Wednesday.
Reached Friday evening, Reds general manager Wayne Krivsky would not confirm that his team landed Cordero.
"There's no deal," Krivsky said. "We've had conversations, I can tell you that. There's nothing to announce. That's where it stands."
But Brewers GM Doug Melvin said that agent Bean Stringfellow informed him on Thursday that Cordero had chosen Cincinnati. Milwaukee offered $42 million over four years with a $13 million option for a fifth year, but apparently came up short.
"It's about setting the bar. Now they have a new bar for relief pitchers," Melvin said. "Francisco is a very good pitcher, and it's definitely going to help Cincinnati and hurt us. ... We thought that we made him a very solid offer. A million dollars a year more, who knows? With these high salaries this year, who knows what is enough. If we would have been at $44 [million] or $45 [million], would he have chosen us? I don't know. We never got the opportunity top go there. [Stringfellow] never came to us and said, 'Will you go there? We had people who thought we were bidding against ourselves last week."
Cordero, 32, was one of the top closers available on the market this winter. In 66 appearances for Milwaukee this past season, he was 0-4 with a 2.98 ERA and 44 saves in 51 chances. He is a two-time All-Star, including in 2007.
According to the source, the Astros were also vying for Cordero's services against Cincinnati and Milwaukee.
A nine-year veteran of the Tigers, Rangers and Brewers, Cordero has 177 career saves and a 3.29 lifetime ERA. He had a career high of 49 saves with Texas in 2004.
Assuming Cordero passes his physical and joins Cincinnati, current closer David Weathers would likely move back into a setup role. Weathers had 33 saves for the Reds in 2007. The club's back end of the bullpen is also bolstered with right-hander Jared Burton, a rookie who emerged as a strong eighth-inning option.
Fixing the bullpen was one of the Reds' top priorities during this offseason. Last season, Cincinnati relievers posted a 23-31 record, a league-high 5.13 ERA and converted 34 of 61 saves.