But it might not be their only trade before Tuesday's Trade Deadline, as clubs have interest in first baseman Justin Morneau and outfielders Denard Span and Josh Willingham.
Twins general manager Terry Ryan wouldn't rule out another trade but wouldn't say how likely it'll be that he'll make another move before the 3 p.m. CT Deadline.
"There's a lot of volume the last couple days," Ryan said. "There's a lot of talks but whether or not it comes to anything I don't know."
Unlike Liriano, who is a free agent after the season, Span, Willingham and Morneau are all signed past this year, so the Twins will be looking for a bigger return if they deal any of the three.
Span, who was also the subject of trade rumors last season, said he's trying not to get too worked up before the Deadline.
"I'd be lying to you If I tell you I don't think about it or it's not on my mind," Span said. "You can't control it. You just hope you can make it through the Trade Deadline. Either way, whatever happens, I'll take it in stride."
Morneau, who is owed $14 million next year, is taking the same approach as Span and indicated he'd like to stay in Minnesota.
"It's out of my control, so whatever happens, happens," Morneau said. "Obviously I'm here, I'm part of this team. I enjoy playing here, this is where I want to be. Outside of that, I can't really control much."