Of that group, Liriano remains the most likely to be traded, as he's the lone player who is eligible to be a free agent after the season.
Now, the Twins are faced with trying to stay focused despite the trade rumors, and it's something general manager Terry Ryan says happens to every team whether it is buyers or sellers.
"It's inevitable," said Ryan, who all but confirmed the Twins will be sellers. "This time of year, that happens. Every team, every organization goes through the same thing. There's not a team in the game that doesn't worry about that at this time of the year."
Liriano remains the club's best trade chip, and the veteran lefty has been solid since returning to the rotation on May 30, after a stint in the bullpen. He struggled in his last start, but has a 3.68 ERA with 79 strikeouts and 29 walks in 66 innings over his last 11 outings.
Scouts from clubs such as the Angels, Blue Jays, Braves, Mets and Yankees have been at his recent starts. And with a lack of starting rotation depth, the Twins will be looking for pitching in return for Liriano.
Liriano, though, said he's trying his best not to get too wrapped up in all the trade talks.
"I try not to listen to it," said Liriano, who is scheduled to start Sunday against the Indians. "It's not going to change anything. I'm just happy to be here. Whatever happens, happens. I don't know what is going to happen. So I try not to pay attention to it."
Several clubs also have interest in Span, Willingham and Morneau, but the Twins want a big return in any trade, as all three players are signed past this season.
Span is signed to a team-friendly deal through 2014 with a club option for '15. And Willingham just signed a three-year, $21 million deal this offseason, while Morneau is owed $14 million next season in the last year of a six-year, $80 million deal inked in '08.
The Twins also lost two potential trade chips in right-hander Carl Pavano and closer Matt Capps, who are both on the disabled list with shoulder-related issues and are eligible for free agency at season's end.
Pavano just started throwing off a mound on Sunday and remains at least a few weeks away from returning, while Capps will be shut down for the next two weeks.
But Ryan refused to look at the injuries as a lost opportunity for the Twins, as he's more worried about them coming back healthy.
"I wouldn't be worried about trade chips when it comes to a guy's health," Ryan said.
But if either of the two prove healthy in August, they could still be dealt after clearing waivers after Tuesday's non-waiver Trade Deadline.
Once the Trade Deadline has passed, deals involving players on the 40-man roster cannot be made unless the players already have cleared waivers. In other words, the player must be offered to the other teams in reverse order of the standings, and if he is claimed by one of the teams, he cannot be traded. The club that placed the player on waivers can either withdraw the request and keep the player, or let the player go to the claiming team, which would then have the rights to the player.