Bobby Parnell’s partially torn medial collateral ligament in his right elbow will cost him at least six weeks with the Mets, and potentially much longer. According to general manager Sandy Alderson, the right-hander’s “conservative” rehab approach will entail about two weeks of rest followed by a throwing program that would last a month, if he is healthy enough to complete it. If the throwing program is unsuccessful, Parnell would be staring at Tommy John surgery, which would sideline him for 12 months. Parnell was diagnosed with the MCL tear on Tuesday, a day after he complained of soreness in his right forearm after blowing a save in the ninth inning against the Nationals. Alderson indicated Parnell had soreness for several days before Monday’s appearance, but didn’t alert the club. “Bobby’s injury is to a thicker part of the ligament, which means the partial tear may not be as serious and immediately require surgery as a tear in another part of the ligament,” Alderson said before the Mets faced the Nationals on Wednesday. “We certainly endorse the conservative approach for the time being. He will rest for a couple of weeks. We should know whether in six weeks or so if this is successful.” Alderson said it may be difficult gauging Parnell’s progress given that his velocity had dipped prior to the diagnosis. “I think the standard initially will be simply, ‘Is he throwing pain-free?’ ” Alderson said. “Later that standard will shift to velocity, breaking pitches, to a level somewhat more demanding than just pain-free.”