If Morneau is claimed before Wednesday's deadline, the Twins can work out a trade with the claiming team, let that team take his contract or pull him back and keep him in Minnesota. If he is not claimed, the Twins are free to negotiate with any team.
Morneau was drafted by the Twins in 1999 and has been a cornerstone of the team for a decade. He is in the final year of his contract.
Morneau declined to comment Tuesday about being put on waivers. Manager Ron Gardenhire said that putting players on waivers is simply a procedural move that the Twins and other teams do with a majority of their players every August.
Right-hander Josh Johnson was put on the 15-day disabled list by the Toronto Blue Jays because of a sore forearm.
Johnson's scheduled start Monday had been pushed back to Wednesday because of the pain. The decision to put him on the DL came after he felt sore while playing catch during batting practice Tuesday.
Acquired from Miami in a 12-player trade in November, Johnson is 2-8 with a 6.20 earned-run average in 16 starts.
Alex Cobb to start for Rays on Thursday
Alex Cobb is expected to pitch for the Tampa Bay Rays on Thursday night, his first game in the majors since being hit in the head by a line drive in June.
Manager Joe Maddon said that the Rays think the right-hander is ready to face the Seattle Mariners.
Cobb (6-2) was struck in the right ear by a liner hit by Kansas City's Eric Hosmer on June 15. He has been on a minor league rehabilitation assignment.
Second baseman Dan Uggla of the Atlanta Braves said he finally realized he could not wait any longer to have surgery to improve his vision and was put on the 15-day DL.
Uggla, batting only .186 with a National League-leading 146 strikeouts, has battled eye problems throughout the season and has experimented with contact lenses.
Uggla's goal had been to postpone the procedure until the off-season. He said he expects to have the procedure done as soon as possible and sit out only two weeks.
Third baseman Mike Moustakas was out of Tuesday night's Kansas City Royals lineup against the Miami Marlins because of a Grade 1 strain of his left calf that he suffered Monday night while running the bases.
Moustakas had an MRI exam that revealed the strain. He hasn't been put on the disabled list, but it was unclear how long he'll be out.
Rangers' Matt Harrison to sit out rest of season
Opening-day starter Matt Harrison won't pitch again this season for the Texas Rangers.
Harrison made only two starts at the beginning of the season before two operations on a herniated disk in his lower back. He had been pitching in rehab games before feeling a twinge in his elbow and numbness in his hand last week.
General Manager Jon Daniels said that Harrison met with the team doctor and the surgeon who did the operations. They determined that Harrison's back wasn't strong enough, and that he was making adjustments in his delivery that led to his symptoms.
Manny Ramirez is released from minor league contract
Manny Ramirez was released from his minor league contract by the Rangers.
Ramirez, 41, hit .259 with three home runs and 13 runs batted in in 30 games for triple-A Round Rock after agreeing to a deal last month.