Minnesota acquired reliever Stephen Pryor from Seattle in exchange for Morales, and it could look to move more pieces before Thursday's Deadline. Several Twins players have popped up recently in trade rumors, including outfielder Josh Willingham, catcher Kurt Suzuki, right-hander Kevin Correia and relievers Casey Fien and Brian Duensing.
General manager Terry Ryan said he's had plenty of contact with other GMs leading up to the non-waiver Trade Deadline, and he believes his club has other tradable assets outside of Morales.
"We've got some people here that there will be interest in," Ryan said. "At this time of the year, you're going to have activity, especially if you're in the situation that the Twins are in right now. It's going to be a little busy now."
Ryan also indicated that with the addition of the second Wild Card in both leagues, it makes it a seller's market simply because of supply and demand.
"It's probably a seller's market, because there's still so many teams still in contention for that second Wild Card," Ryan said. "There's a lot of teams that are only four or five games out."
Willingham, 35, is in the last season of a three-year, $21 million deal signed before the 2012 season, and he has grown accustomed to hearing his name mentioned in trade rumors. He's struggled a bit this year, but he still provides power from the right side and is only two years removed from hitting 35 homers and winning an AL Silver Slugger Award.
But Willingham said he just tries to tune everything out and doesn't worry too much about the Trade Deadline.
"I pay seriously zero attention to it," Willingham said. "What I do hear comes from teammates or my wife, but I really don't pay any attention to it."
Suzuki, 30, is in the midst of perhaps his best season, and he was named an All-Star for the first time in his career. Several teams, such as the Orioles, could be looking for an upgrade at catcher, and Suzuki has been getting rave reviews from the Twins for his ability behind the plate to go along with his career year offensively.
But the Twins could decide to hold onto Suzuki, especially if they decide they'd like to extend his contract, which ends after the season. Catching prospect Josmil Pinto's bat is Major League ready, but he still has plenty of work to do defensively, so that plays into Minnesota's decision.
Suzuki has remained noncommittal on the issue, but said he has enjoyed his time with the Twins this season.
"I haven't thought that far down the road," Suzuki said. "I've really enjoyed my time here, with a great group of guys, a great coaching staff and a great front office. So I'm just trying to have fun and take it day by day. Sometimes you can get caught up in that stuff."
Correia, who is in the second season of a two-year deal worth $10 million, also might garner some interest, but the 33-year-old hasn't helped his cause with two subpar outings after the All-Star break. Correia, who had a 3.22 ERA spanning 11 starts until turning in his two recent subpar outings, now has 13 losses and a 5.06 ERA on the year.
Teams with interest in a right-handed setup man could also look to Fien, while those in need of a left-handed reliever could turn to Duensing. There hasn't been as much buzz around those two, but both are having solid seasons out of the bullpen.
Even if Minnesota doesn't make any additional moves before the Trade Deadline, it doesn't mean the club can't make trades after July.
Once the non-waiver 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.
The Twins have made a few notable August trades in recent seasons, such as sending Jim Thome to the Indians in 2011, dealing Delmon Young to the Tigers that same year, and trading Justin Morneau to the Pirates last season.