Morse has missed three games with a strained quadriceps muscle in his right leg.
"I'm hoping we can start Smoaker tomorrow," Wedge said prior to Saturday's game. "We'll probably stay away from Morse another day, and then we'll take some BP tomorrow and see how he is then."
Smoak pinch-hit on Wednesday in San Diego in a situation where he could swing right-handed, but the switch-hitter continues to be hesitant to swing fully left-handed and re-aggravate the injury. The Twins are starting southpaw Scott Diamond on Sunday, so Smoak will be able to hit right-handed in that game.
The Mariners will also see lefty John Danks on Monday in Seattle when they host the White Sox, but then they'll face a pair of righties -- Jake Peavy and Dylan Axelrod -- on Tuesday and Wednesday.
Greg Johns is a reporter for MLB.com. Follow him on Twitter @GregJohnsMLB as well as his Mariners Musings blog. This story was not subject to the approval of Major League Baseball or its clubs.