With Storen reportedly out of the picture, it appears less likely the Twins would want to trade Span, who has been out with a concussion suffered on June 3 in a home-plate collision with Royals catcher Brayan Pena.
Span was one of the club's best players before his injury, hitting .294 with a .361 on-base percentage while providing excellent defense in center field. He's also signed to a team-friendly deal, as he inked a five-year, $16.5 million contract through the 2014 season that began last year. The contract also includes a $9.5 million team option for '15.
He played nine innings in center field for the first time as part of his rehab process with Triple-A Rochester on Wednesday and did the same on Thursday, going 1-for-4 with a stolen base.
"He's continuing to do well," Twins trainer Rick McWane said. "There are no issues with the concussion."
Span, who didn't play on Monday or Tuesday, still needs to play four to six full games in a row before he's ready to be activated from the disabled list, according to Twins manager Ron Gardenhire.
"He had a couple days off, so I'm hoping he's feeling pretty good," Gardenhire said. "He should be. So we'll go from there. That's when you're starting to feel the up and up, playing back-to-back ballgames"