While rival teams were suggesting they viewed the Mets as a big player for Japanese ace Yoshinobu Yamamoto, many believe that is far from a certainty with every big-spending team in the mix.

The Mets aren’t assuming anything and are showing interest in other free-agent pitchers, including Blake Snell, Jordan Montgomery and Eduardo Rodriguez. Among the fallback options, they may have a possible preference for Snell.

The Yankees also are hopeful on Yamamoto but have only been linked to former Yankee Montgomery as a star pitching option.

The Red Sox are in on Montgomery, but the incumbent Rangers are seen as the favorite for now.

One report by Susan Slusser of the San Francisco Chronicle suggested several teams envisioned the Giants as a strong fit. The Giants are also going hard for Ohtani, and that could impact their pursuit of Yamamoto.

Former Met Seth Lugo could wind up with the Mets’ main nemesis in Atlanta. The Braves are one of the teams in the bidding for the free agent.

The Red Sox, Reds and Diamondbacks also have shown interest in Lugo.

The Cubs are looking at Matt Chapman and their own Cody Bellinger, but waiting on Ohtani first.

The Cubs also have interest in Rhys Hoskins since Pete Alonso probably isn’t going anywhere.