Gutierrez took batting practice with the team for the first time on Tuesday. He'll continue working with the team this week, then fly to Arizona on Sunday and begin playing extended spring training games with Minor League players on Monday.
Manager Eric Wedge said he expects Gutierrez will play five or six days in Peoria before going out on a Minor League rehab assignment with either Double-A Jackson or Triple-A Tacoma. Once his rehab starts, he'll have a maximum of 20 days, per Major League rules, before he'll need to be recalled.
Thus, if all goes well and Gutierrez stays on schedule, he'd likely be back with the Mariners in late June.
Asked if he was pleased with Gutierrez's progress this week, Wedge said: "I'll be pleased when he's back with us."
In the meantime, Wedge has been happy with the performance of Michael Saunders in center field in the absence of the Gold Glover.
"He's real good out there," Wedge said. "This is a guy who really worked hard last year, and arguably improved as much as any outfielder. If you talk about being comfortable, getting to be pretty good, getting to be good and then getting to be better than that, that's what we've seen with him."