In the spring, the Giants reportedly offered Sandoval a three-year, $40 million contract, which he rejected, and after he collected 26 postseason hits, and caught the final out of the World Series, he has made the decision that much harder.

“Look, we’ll do the best we can,” Larry Baer, the Giants’ chief executive, told reporters when asked about the situation. “And up till now, the best we can has been to secure our guys.”

A two-time All-Star with a .294 career batting average, Sandoval, 28, is an intriguing case because he has not performed at an elite level over the last several regular seasons and has the type of heavyset body that does not usually remain resilient.

The Boston Red Sox, a team that could pursue Sandoval aggressively in light of their needs at third base, wrote the blueprint for succeeding without sentimentality by letting Pedro Martinez walk after they won the World Series in 2004. Like Sandoval, Martinez was a colorful and popular player, but the Red Sox determined that paying top dollar would be unwise. The move worked out well for Boston, as Martinez managed 30 or more starts just once in his last five seasons.

If the Giants make a similar decision, their Panda-hatted fans may not be as accommodating as the Red Sox fans were about saying goodbye to their idol.