The Minnesota Twins aren't going to be without catcher Joe Mauer, despite Ken Rosenthal's reports via Twitter that Mauer has cleared waivers and can now be traded by Friday at midnight. He also notes that it is very unlikely that any kind of trade is made. Mauer has a full no-trade clause in his contract, and while the team could still work out a deal pending Mauer's approval, it doesn't seem like that's something they're considering at this point.
The Twins placed Mauer on revocable waivers, which made him available to other teams. There was rumors about the Boston Red Sox potentially being interested, but no team submitted a claim. Had a team claimed Mauer, the Twins would have had the opportunity to pull Mauer from the waivers, or negotiate a trade with the team that claims him. As a third option, they could have let the team have him for nothing, but that was always unlikely.
It's still unclear if the Twins are hoping to move Mauer and his $142 million contract, but most are of the opinion that this is unlikely.