They seemed so congenial after the Super Bowl. (John Samora / The Arizona Republic via AP)

U.S. District Court Judge Richard Berman has ordered Tom Brady and Roger Goodell to “engage in good faith talks” Tuesday before he presides over arguments in their case Wednesday in New York.

“In anticipation of tomorrow’s conference, counsel and the parties are requested to engage in further good faith settlement efforts today,” Berman wrote in his brief order. “I will meet briefly with counsel and the parties tomorrow morning at 10:30 (in the robing room) for an update on your discussions.”

The document was filed Monday morning and once again makes clear how strongly Berman wants to see the parties to DeflateGate settle this case, as he has been urging virtually since the moment he drew the case by lottery. On July 30, when he ordered both sides to appear in court, he urged them to “tone down their rhetoric” and “begin to pursue a mutually acceptable resolution.”

[Don’t expect a Brady settlement by NFL, NFLPA]

Berman may have used the word “requesting,” but it’s a much stronger command than that. Still, it’s not terribly likely to happen, as The Post’s Mark Maske reported.

“I don’t see much willingness to move toward a middle ground,” one of those people said, speaking on the condition of anonymity because the case is in court.

Another person familiar with the case expressed similar sentiments, saying: “You never say never, I guess. [But] I don’t expect it.”

The order means that he wants each side as close as it can get to its final, no-wiggle-room position. That way, he won’t have to listen to a lot of negotiating. Then, when he knows where each side stands, the hearing on the case’s merits will proceed.

The next court date presently set is Aug. 19. The NFL and the NFL Players Association hope for resolution of the case — and Brady’s four-game suspension — before the Patriots open the season Sept. 10 against the Pittsburgh Steelers.