Charles D. Baker, president and CEO of Harvard Pilgrim Health Care

Chance of running: Not high. “I have no interest in a senate seat,” he said. “It’s not a great job for me.”

Pro: Made his reputation in administrations of governors William F. Weld and Paul Cellucci, and is seen as a formidable candidate.

Con: He is seen by state Republican leaders as one of their best chances to recapture the governor’s office, and a Senate bid would distract from those efforts. As a nonprofit healthcare executive, he would not be able to raise political funds or carry out political activities.