But if any team has made such an offer, it's hard to figure out who it is. Though at least four teams are pursuing closers, virtually all of them have made it clear that they have little taste for going to those sorts of lengths in order to sign a ninth-inning pitcher.
So while Fuentes is by far the top free-agent ninth-inning man available, it's tough to see the ongoing chase turning into an endgame soon. The number of teams that might be interested in Fuentes is quite a bit higher than the number of teams that are known to be actively bidding.
John Mozeliak is the general manager of the Cardinals, the team reported in some circles to be the leader for Fuentes' services. But Mozeliak said on Thursday on his way out of the Bellagio that the Cardinals would be extremely hesitant to commit even $10 million per year to a relief pitcher, never mind $11 million.
The Angels may well be a player after losing Francisco Rodriguez. They are mostly fixated on retaining first baseman Mark Teixeira, but Fuentes is on their radar. But general manager Tony Reagins seemed a bit shaken by what he perceived the bidding numbers to be for the lefty late of the Rockies. Reagins described the market for Fuentes as "aggressive" on Thursday.
Tigers general manager Dave Dombrowski virtually took his team out of the bidding on Thursday. Dombrowski said that the Tigers likewise won't go to eight figures for Fuentes or any other reliever, and he indicated that Detroit probably won't be a player for any of the top remaining free-agent closers -- a group that basically includes Fuentes and Trevor Hoffman.
Also in the market for a ninth-inning pitcher are the Brewers and potentially the Nationals. Milwaukee, however, is more focused on finding starting pitching right now, and may go a more creative route than signing a big-name free agent. The Brewers did meet with Thurman, but the Brewers' interest is not overwhelming at this point.
So in the end, the situation appears to favor the Cardinals, who have acknowledged that they are at least a little ways down the road in negotiations with Fuentes. They met with not only Thurman but Fuentes himself this week, and manager Tony La Russa made it very clear that Fuentes is his team's top priority.
"I don't get into offers and that type of thing, but I would characterize it as, it's more than just exploration at this point," said Mozeliak, who typically remains fiercely tight-lipped about the progress of any ongoing negotiations.
It still appears unlikely that a deal for Fuentes will get done imminently -- unless, of course, someone meets that rumored price tag that nobody seems eager to touch.