As the final month of his final season played out, Paul Konerko relished the peaceful ending to his proud career. There was enough hoopla out of the public view, anyway, and he did not want the parting gifts and ceremonies bestowed on other stars.

“No, no — God, no,” Konerko, the longtime Chicago White Sox first baseman, said next to his locker before a game in September 2014. “I mean, listen — I knew when I signed to come back I was going to have to deal with some of the stuff that goes along with it. I didn’t really put that in the pro column — more of the con column. Because it’s all about the game on the field, and you want to just feel like one of the guys.”

Konerko was enough of a regular guy — despite 439 home runs and 18 major league seasons — to retire without much fanfare. For David Ortiz, who has commanded attention for 13 seasons with the Boston Red Sox, things just might be different.

Ortiz turned 40 Wednesday, which seems like the right time to announce that 2016 will be his last season in the majors. Ken Rosenthal of MLB Network and Fox reported on Tuesday that Ortiz had decided that would be the case, though there was no formal announcement.

Ortiz told The Boston Globe last spring that people close to him had recommended he announce his retirement in advance, to capitalize on endorsement potential. Ortiz was not sure he wanted a farewell tour, but his status in the game might leave him no choice.

Throughout the 2012 season, rival teams saluted the Atlanta Braves’ Chipper Jones as he made his final visits around the league. They did the same over the next two seasons for two decorated New York Yankees: Mariano Rivera in 2013 and Derek Jeter in 2014.

Last season, the ending came for Jeremy Affeldt, A.J. Burnett, Dan Haren, LaTroy Hawkins, Tim Hudson, Torii Hunter, Aramis Ramirez and Barry Zito. All played admirably for a long time, but none with the outsize impact of Ortiz.

Away from Boston, Ortiz is not always held in the tip-your-cap esteem that Jones, Rivera and Jeter were. He was flashier (those bat flips!) and more petulant (that poor dugout phone in Baltimore!), and for many, he wore the notorious scarlet S of the steroid era.

Ortiz tested positive for performance-enhancing drugs in 2003, when the results were supposed to be anonymous and players were not subjected to penalties. When The New York Times revealed the positive test in 2009, Ortiz said that the players’ union had confirmed to him that the report was true but that he was surprised because he had never knowingly used banned drugs.

That episode complicates Ortiz’s reputation in a way that Jones, Rivera and Jeter never had to endure. But it is also true that Ortiz has never served a suspension for performance-enhancing drugs, and he won baseball’s most prestigious community-service award, named for Roberto Clemente, in 2011. Most important, perhaps, is that Ortiz has been memorable — and really, really good.

He has style, from the chin-strap beard to the spitting-in-his-batting-gloves ritual to the skyward point after home run trots. He has 503 career homers; with 19 more, he would pass the Hall of Fame threesome of Ted Williams, Willie McCovey and Frank Thomas and vault into the top 20 on the career list.

And he has risen when his team needed him most, with a .455 average in three World Series, all resulting in championships for a franchise that had gone more than eight decades without one before he arrived.

So many stars of this generation have taken after Jeter, and that is mostly a good thing. They are polite, accommodating and somewhat bland, making them safe spokesmen for the game. Ortiz is a wise hitter and a sound mentor to younger Red Sox, but he can also be profane and outrageous, and he is no model for hustling down the first-base line.

Yet Ortiz has been tough enough to thrive in a market that has suffocated others, and he is a certified winner. Nobody looks away when he comes to the plate. Children are drawn to him, and he interacts easily with them. The game needs more players with his charisma and magnetism.

So is it settled, then? Can Ortiz get a farewell tour like Jones, Rivera and Jeter? Let’s hope so.

Those three left the stage with a mountain of goodies from around the majors: The Tampa Bay Rays gave Jeter a pinstriped kayak; the Minnesota Twins gave Rivera a rocking chair made of broken bats; the Milwaukee Brewers gave Jones a grill and a year’s supply of sausages.

Ortiz will finish the regular season at Fenway Park against Toronto on Oct. 2, after playing on the road in 18 cities. The last stop, from Sept. 27-29, is the Bronx.

Ortiz has hit .316 at the new Yankee Stadium, matching his best average at any park in which he has played at least 20 games. New York fans might suggest that the Yankees give Ortiz something he rarely saw from them — high, inside fastballs — but that would accomplish little.

By now, Ortiz’s legacy is secure: Big Papi equaled big impact, in every way.