MILWAUKEE — Let’s use the term “mildly aware” to describe Jonathan Lucroy and Mets fans’ interest in bringing him aboard the defending National League champions.

“Little bit,” the Brewers catcher, whose Twitter account gives him a direct pipeline to the public, said Saturday, before Milwaukee pounded the Mets, 7-4, at Miller Park. “Not really. It’s just fans. That’s just part of the game, I guess.”

Here’s the current state of the game: The rebuilding Brewers really should trade Lucroy, who can be a free agent after next season. The contending Mets really could use better offensive production from their catching position, among other places.

So will we see a deal? It won’t be easy, for two reasons:

1. The Mets don’t sound ready to give up on Travis d’Arnaud as their long-term catcher.

2. The Brewers, who can ask for plenty to land Lucroy, and the Mets, whose best young talent already is playing crucial roles on the major-league club, might not have a match.

As of Saturday, Mets vice president and assistant general manager John Ricco said, “We haven’t really talked about going out and getting catching. … That’s not something that’s on our list right now.”

D’Arnaud, who has been out since April 26 with a strained right rotator cuff, started at catcher for Single-A St. Lucie and played seven innings on Saturday night, a significant step; he had been DHing for St. Lucie since last week. The 27-year-old has missed time due to injury every year since the Mets acquired him and most years before he became a Met. Nevertheless, his career .719 OPS in the big leagues, strong for a catcher, makes the Mets reluctant to toss him aside.

“I think between Travis and [Kevin] Plawecki, we’re still very confident both of them are going to be very good players,” Ricco said. “I believe catching is the one position you have to have a lot of patience with, because you throw so much at the young catchers, both offensively and defensively, and they have so many responsibilities.

“The injuries are obviously something Travis is going to have to overcome to stay on the field. But between the two of those guys, I think we’re still really confident that we have two good ones.”

Before he suffered his injury, d’Arnaud had put up a terrible .549 OPS in 52 plate appearances. Throw in underwhelming production by Plawecki (.577) and Rene Rivera (.512), and the Mets’ catchers’ collective wRC+ (a metric that evaluates batters, with 100 being average) of 61 through Friday — that is 39 percent below the league average, after factoring park effects — ranked 14th in the National League, with only the Reds (57) worse (thanks, FanGraphs).

Lucroy, who didn’t play Saturday, owns an .876 OPS for 2016 and .778 for his career. He carries a reputation as a sterling defender and great teammate. Thanks to a long-term deal he signed in 2012, he’s drawing $4 million this year and has a $5.25 million option for 2017, making him one of the industry’s greatest bargains.

New York City native David Stearns, the Brewers’ first-year general manager, already has unloaded many of the veteran players he inherited. Lucroy looks like his big summer piece, and given Lucroy’s production and his salary, the asking price should be considerable. The Mets very likely don’t have a minor league pitcher good enough to serve as a primary piece in a trade. Shortstop Amed Rosario? Here’s betting Milwaukee could do better. Jon Heyman of FanRag Sports mentioned the Rangers and Cubs as other possible landing spots.

Lucroy, a polished veteran, said the usual stuff about not expending energy on stuff beyond his control. I asked him how he felt about New York City.

“I’m not really a big city guy,” he said. “I grew up in a small town in Florida [Umatilia]. I like peace and quiet. I like not a lot going on around me. But I do enjoy going there for a few days and playing a series.

“I didn’t enjoy it much this year, because their pitching staff is pretty good. That’s a tough thing. I’ll be glad to see them out of here by [Sunday], because they have one of the best overall pitching staffs I’ve seen personally in a long time.”

It would be even better with Lucroy, his enjoyment of peace and quiet notwithstanding, catching them. That scenario currently exists as more of a Twitter dream than anything else. As long as Lucroy toils for the Brewers, however, the dream can stay alive.