It looks as if Tom Brady will miss the first four games of the 2016 season. (Steven Senne/Associated Press)

A federal court on Wednesday denied New England Patriots quarterback Tom Brady’s request for an appeal of an April ruling that upheld his four-game Deflategate suspension, leaving him with one last, unlikely hope: The U.S. Supreme Court.

As it stands today, Brady will miss the first four games of the 2016 NFL regular season. Backup quarterback Jimmy Garoppolo will take his place alongside the Patriots’ offensive starters. New England opens the season Sept. 11 at the Arizona Cardinals.

Brady and the NFL Players’ Association were asking for either of two things: That the three-judge appeals panel that upheld Brady’s four-game NFL suspension in April rehear their arguments, or for an en banc hearing. In other words, that the entire U.S. Court of Appeals for the Second Circuit hear his appeal of the three-judge panel’s decision, which allowed the NFL Commissioner Roger Goodell’s suspension of Brady to stand, overturning a lower-court decision.

The court shot down both requests.

The NFL Players’ Association issued a statement condemning the court’s decision.

The NFL Players Association is a labor Union that protects the rights of all of its members and pursues any violations of those rights by any means necessary. We are disappointed with the decision denying a rehearing, as there were clear violations of our collective bargaining agreement by the NFL and Commissioner Roger Goodell.

Despite today’s result, the track record of this League office when it comes to matters of player discipline is bad for our business and bad for our game. We have a broken system that must be fixed.

We will review all of our options carefully on behalf of Tom Brady and all NFL players.

Brady’s appeal was a long shot, as both panel rehearings and en banc hearings are approved on only a small number of cases. Seven of the 13 active judges on the court would have had to agree to rehear the case, which apparently did not happen.

“Courts of appeal typically reserve en banc rehearing for cases of broad significance in which reconsideration of the original panel ruling seems necessary to correct error or to clarify some point of law,” Boston College law professor Alfred C. Yen told The Post’s Mark Maske in May. “In this case, the original Second Circuit opinion follows fairly well settled law, with the possible exception [of] Commissioner Goodell’s alleged bias as an arbitrator. The entire Second Circuit could conceivably interpret the original panel decision as one of broad significance, but I would think this fairly unlikely.”

NFL Media’s Ian Rapoport reported Wednesday that Brady and his legal team are expected to petition the Supreme Court to hear their case, and CBS Sports’ Jason La Canfora wrote that Brady and his legal team are “holding internal discussions and weighing options.” Here’s how their next step will look should they choose to take it, per sports-law expert Daniel Wallach.

Assuming that happens, Brady would then need to petition U.S. Supreme Court Justice Ruth Bader Ginsberg, who handles Second Circuit rulings, “to stay the suspension until the U.S. Supreme Court has acted on the case,” Sports Illustrated legal expert Michael McCann wrote earlier this year.

McCann continues:

In seeking a stay, Brady would argue that he would suffer “irreparable harm” in the event that he serves the suspension only to see it vacated later by a court. He would emphasize that he could never get those games back, even if he later wins the appeal. Further, Brady would contend that missing those four games would irretrievably damage his career and, by hurting the Patriots, harm Brady’s teammates and coaches.

But, again, it’s a long shot:

Unfortunately for Brady, stays are extraordinary measures and are seldom granted, and the Supreme Court only considers approximately 1% of petitions. I know this from experience and it connects to the NFL. I was a member of Maurice Clarett’s legal team in his antitrust lawsuit against the NFL over its eligibility rule. After the Second Circuit ruled against Clarett, Clarett petitioned Justice Ginsburg for a stay. It was quickly denied.

Wallach says that Brady has until Oct. 13 to file his Supreme Court petition.

McCann isn’t alone in thinking that Brady is most likely out of options. Here’s Tulane sports-law expert Gabe Feldman:

There’s also the matter of timing. With the Supreme Court on summer vacation, it likely wouldn’t even consider Brady’s case until late September, after the NFL season has begun.

In an e-mail sent to reporters, Yen applied all sorts of sports analogies to describe Brady’s dire-looking situation:

I don’t think there anything here that’s so enticing that I expect the Supreme Court to take this case. It’s possible that the Second Circuit’s ruling on the appointment of Commissioner Goodell as the arbitrator could provoke a little discussion but if the Supreme Court is interested in that issue, I don’t think that this particular case is a case in which they would be likely to take the issue up.

Brady and his legal team are in bad shape. It’s 4th and 15 and you’re on your own 35 yard line and there’s six seconds left in the game.

Brady and the Patriots seemed to anticipate all of this happening when they renegotiated his contract in February.