Tim Lincecum, the Giants’ two-time Cy Young Award winner and one of the most popular players in team history, tentatively plans to pitch in a showcase in the first two weeks of February hoping to land a big-league job, his agent said Friday.

“He’s throwing every day and says he’s doing great,” said Rick Thurman of the Beverly Hills Sports Council. “He’s got no instability in his hip, and he’s enthusiastic about his progress.”

Thurman said that almost all of the 30 teams have contacted him about Lincecum and that at least 20 have requested medical information, adding he wouldn’t permit his client to throw in a showcase until Lincecum is 100 percent. It’s also a matter of getting in baseball shape.

As Thurman noted, “There was never anything wrong with his arm.”

Lincecum, 31, who last pitched for the Giants on June 27, underwent hip surgery Sept. 3 at the Steadman Clinic in Vail, Colo. He hired a company recommended by the clinic, Sports Rehab Consulting, which is run by physical therapist Brad Schoenthaler, who has closely monitored Lincecum’s Arizona-based rehab.

The hope and expectation for Lincecum, whose ERA the past four years was 4.68, is that a repaired hip will get him back on track with his velocity and command.

“Tim’s doing great,” Schoenthaler said. “He looks really strong. His hip pain and compensation patterns have cleared up. Everything’s coming back a lot quicker than we expected.”

Lincecum is expected to begin throwing off a mound within a week, according to Schoenthaler, who works with him 3 to 3½ hours daily on throwing, rehabbing and strengthening and said Lincecum demonstrates “remarkable power” in his hip, trunk and shoulder.

“I feel he’ll walk into spring training stronger or as strong as he normally walks into spring training,” Schoenthaler said. “I think he’ll be plenty strong to be a starter.”

The showcase will be in Arizona. Thurman wouldn’t say what kind of contract Lincecum is pursuing, but the pitcher clearly would seek a major-league deal. A minor-league contract would keep him off a 40-man roster.

The Giants’ rotation is set with newcomers Johnny Cueto and Jeff Samardzija joining Madison Bumgarner, Jake Peavy and Matt Cain. Nevertheless, general manager Bobby Evans has stayed in contact with Thurman and most recently reached out a week ago.

“Timmy has been such a big part of our fabric and success,” Evans said. “It’s important we do our due diligence. Of course we’re going to keep in touch with Tim Lincecum.”

But if Lincecum is healthy and impresses teams in his showcase, he could get offers to join big-league rotations, in which case his days as a Giant would be over. For now, the Giants’ only competition for pitching jobs is in the bullpen.

In the surgery, Dr. Marc Philippon shaved bone matter to relieve an impingement and repaired a torn labrum. After surgery, Philippon — who performed hip surgeries on Alex Rodriguez, Troy Tulowitzki and Warriors draftee Kevon Looney — said he expects Lincecum to pitch in the majors in 2016.

Lincecum won 108 regular-season games for the Giants, struck out at least 200 batters four straight years and was a key figure in their 2010 and 2012 championships. He became a free agent after his two-year, $35 million contract concluded.

John Shea is a San Francisco Chronicle staff writer. E-mail: jshea@sfchronicle.com Twitter: @JohnSheaHey