A certain amount of sex appeal exists among the list of managerial free agents, but are the Mets willing to choose such a path?

First things first: Mickey Callaway remained in place as manager Monday, as team officials look to resolve his status and that of his coaches within the coming days. Despite the fact he is signed through 2020, Callaway appears on slippery footing after avoiding an early-season firing and failing to lead the Mets to the postseason.

The Angels became the latest team with a managerial vacancy after firing Brad Ausmus on Monday. The Cubs, Pirates, Giants, Padres and Royals are also searching for new managers.

If the Mets fire Callaway, the internal debate will begin between the merits of an experienced manager versus unearthing next year’s version of Rocco Baldelli, a novice who guided the Twins to 101 wins in his first season.

Joe Girardi has told intermediaries he would be willing to listen if the Mets job opens, according to an industry source, and Buck Showalter — another accomplished manager with a New York pedigree — is somebody general manager Brodie Van Wagenen likes and considers capable of making a splash, according to another source. But the Mets in recent managerial changes have also largely avoided giving serious consideration to big names.

Part of it might be the financial aspect. The Mets haven’t paid a manager as much as $2 million a year since Willie Randolph was finishing his final contract a decade ago. Since then, it’s been Jerry Manuel (who replaced Randolph in-season), Terry Collins and Callaway, the latter two of whom arrived with at least something of a rebuild needed. In Collins’ case it was a total reconstruction needed.

Now, the Mets have Pete Alonso, Jeff McNeil and Jacob deGrom, a nucleus in place for possible instant success, provided other pieces are added. Would such readiness increase the chances of Van Wagenen making a splash at manager?

In addition to Girardi and Showalter, Joe Maddon is another intriguing available name. Maddon, who won a World Series with the Cubs after guiding the Rays to a pennant, will interview with and is the strong front-runner for the Angels, where he began his coaching career (included was a stint under Collins in the late 1990s). Maddon’s communication skills are exceptional and he would certainly excel in dealings with the New York media.

Girardi has gushed over the Mets’ talent during his cameos at Citi Field for Fox broadcasts. With the tightly wound Girardi, there would be questions whether he could coexist with a hands-on front office. How would Girardi react to receiving a message from the GM during a game telling him to pull deGrom because of an injury concern — as The Post reported happened this season with Callaway in the dugout.

And maybe that would put Showalter more in play for the Mets than Girardi.

“Buck is one of the best politicians I’ve seen,” said a longtime acquaintance of the former Yankees, Diamondbacks, Rangers and Orioles manager.

If the Mets want experience without the star power, Ausmus, Bob Geren, Mike Matheny and John Gibbons are among the names that could be considered. The Mets contacted Ausmus during their managerial search two years ago, but the Cheshire, Conn., native declined to interview and sat out the year before accepting the Angels job last offseason. Geren certainly knows the Mets landscape after serving as Collins’ bench coach for four seasons. He’s spent the past four with the Dodgers as Dave Roberts’ top lieutenant.

Lastly, there is the novice route. In house, the Mets are high on quality control coach Luis Rojas, and names such as Astros bench coach Joe Espada, MLB Network’s Mark DeRosa and Rays bench coach Matt Quatraro could be considered.

First, the Mets have to announce whether they are moving on from Callaway.