The Twins are sprinkling rehab assignments all over their minor league system.

Outfielder Josh Willingham, who had left knee surgery June 3, will join Class AAA Rochester in time for a series at Durham, N.C., on Monday. Willingham, while also dealing with a bone bruise in his left knee, had a torn meniscus repaired. He returned to batting practice this week and is ready to play in rehab games. Willingham will DH and play left field for the Red Wings.

Willingham could return in time to impress teams looking for some pop before the Aug. 31 deadline for waiver trades.

Outfielder Wilkin Ramirez, who hasn’t played in the majors since May 25 because of a concussion, has been playing for the Gulf Coast League rookie team but will move to Class AA New Britain this weekend.

Outfielder Darin Mastroianni (left ankle surgery), who was playing with Ramirez for the GCL Twins, will move to Class A Fort Myers.

Ramirez and Mastroianni will play all three outfield positions.

“We’re trying to spread it out so they will get the opportunity to play at different positions,” General Manager Terry Ryan said.

Morneau’s options

First baseman Justin Morneau has twice reached out to the Twins about a contract extension and been turned down both times. He remains with the team following the nonwaiver trade deadline Wednesday and now must go through the Aug. 31 deadline in which players can be dealt after clearing waivers.

Morneau’s .174 batting average in July surely contributed to the lack of a market for the 2006 AL MVP. Things could change with a big August. And Morneau got the month off to a good start with a home run to center field in the third inning Thursday estimated to have traveled 410 feet.

If Morneau isn’t dealt by the end of August, the Twins could approach him about signing then. But most players in their free-agent year end up testing the market to see what their value is, and Morneau might choose to look around — which doesn’t guarantee he would return to the Twins.

“I think if I get to the point where I’m a free agent, I’m probably going to explore my options and see what happens, if anyone is a fit for me,” Morneau said, “but that is so far in the future. We still have a couple months of baseball left, and [we] gotta finish the year well and continue with this organization moving in the right direction.”

Compensation for Butera

The Twins have six months to find out who they will receive for Drew Butera, who was traded to the Dodgers on Thursday. The player will not be from the Dodgers’ 40-man roster.

In many deals in which a player to be named is involved, one club provides a list of players from which the other team can choose. The Twins have such a list from the Dodgers. Ryan said the club is not looking for cash in the deal, but it is required by the league to be included in case the player gets injured.

Catcher Josmil Pinto has been promoted to Rochester to take Butera’s spot on the roster. Pinto batted .308 in 107 games at Class AA New Britain with 14 homers, 68 RBI and a .411 on-base percentage.

Ryan to get award

Ryan will be in Philadelphia on Friday to accept the Roland Hemond Award, given to the baseball executive who has demonstrated a lifetime commitment to professional baseball scouts and scouting, and player development history.