NEW YORK – One by one, for three weeks already, players accompanied by their lawyers have been summoned to interviews as part of baseball’s latest investigation into performance-enhancing drugs — and the process is a long way from finished.

Some pretty big names, led by Alex Rodriguez, could be on the hot seat.

A-Rod, Ryan Braun, Nelson Cruz, Melky Cabrera and Bartolo Colon are among the 20 or so players who may be disciplined for their links to the now-closed Miami anti-aging clinic, Biogenesis of America.

The players’ union says it has been assured no decisions regarding discipline will be made until the interviews are completed.

Interviews with players started last month and are scheduled until the end of June, according to sources.

Lawyers in baseball’s labor relations department conducted several interviews, and some players haven’t yet been scheduled.

“Every player has been or will be represented by an attorney from the players’ association,” union head Michael Weiner said. “The players’ association has every interest in both defending the rights of players and in defending the integrity of our joint (drug) program. “

MLB has been seeking the cooperation of Biogenesis founder Anthony Bosch since the Miami New Times reported in January that it obtained what the paper said were records detailing drug purchases by Rodriguez, Cabrera, Cruz and Colon. Yahoo Sports reported that Braun, the 2011 NL MVP, was mentioned in the records.

MLB sued Biogenesis and its operators in a Florida court in March, an attempt to pressure Bosch. MLB wants to speak with Bosch in the next few days,

Among the players linked to the clinic, Cabrera, Colon and San Diego catcher Yasmani Grandal already have served 50-game suspensions following positive tests for testosterone.

“It looks like it could be getting to the bottom of this and finding some information that hopefully would help Major League Baseball as far as cleaning this game up,” said San Francisco Manager Bruce Bochy, who managed Cabrera last year. “I’m all for stiffer penalties.”

WHITE SOX: Jake Peavy will miss at least the next four to six weeks after an MRI revealed the Chicago starter has a non-displaced rib fracture on the left side of his chest.

INDIANS: Drug agents in Ohio are investigating a suspected marijuana shipment to the home of closer Chris Perez.

No one has been arrested. Perez hasn’t commented.

PHILLIES: Erstwhile ace Roy Halladay remains optimistic that he’ll pitch in 2013 after undergoing shoulder surgery in mid-May. The Phillies estimated a six-to-eight-week period of rest.

NATIONALS: Top-of-rotation pitcher Stephen Strasburg went on the 15-day DL with a strained back muscle.

ROCKIES: An MRI showed no serious problem in Tyler Chatwood’s pitching arm, leaving Colorado optimistic he might miss only one start.

REDS: Right-hander Johnny Cueto went back on the 15-day DL with a sore muscle by his pitching shoulder, the second time this season that Cincinnati has lost its top starter to the injury.