"Given the NFL's history of inconsistency and arbitrary decisions in disciplinary matters, it is only fair that a neutral arbitrator hear this appeal," the association said in a statement.
But late Thursday, the league said that Commissioner Roger Goodell would rule on the matter.
"Commissioner Goodell will hear the appeal of Tom Brady's suspension in accordance with the process agreed upon with the NFL Players Association in the 2011 collective bargaining agreement."
The league has said the suspension is a fair punishment
The team was fined $1 million and will forfeit its first-round selection in the 2016 NFL Draft and its fourth-round pick in the 2017 draft.
The appeal isn't a surprise. Brady's agent, Don Yee, had promised one on Monday when the National Football League suspended Brady for four games without pay. That move came after an investigation found that the Patriots used underinflated footballs for an advantage in last season's AFC Championship game.
"The discipline is ridiculous and has no legitimate basis," Yee said in a statement Monday.
"In my opinion, this outcome was predetermined; there was no fairness in the ... investigation whatsoever," he said. "There is no evidence that Tom directed footballs be set at pressures below the allowable limits."
But a report by attorney Ted Wells
, hired by the league to investigate the incident, found that
Brady probably had at least a general knowledge about how the balls were deflated. The report points its finger at equipment assistant John Jastremski and the man who carried the balls from the officials locker room to the field, Jim McNally, as the likely perpetrators.
Brady, when interviewed, denied knowing about or being involved in the deflation efforts. He said recently at a public event that the team earned everything during its Super Bowl-winning season.
It isn't clear exactly when his representatives will be making their case to the NFL.
Any appeal hearing will begin within 10 days of the league's receipt of an appeal. Brady's appeal would be heard by either NFL Commissioner Roger Goodell or an officer of his choosing.
Patriots: Belief in Brady 'has not wavered'
The Patriots are standing by their quarterback, calling the discipline one-sided.
"Tom Brady has our unconditional support," the team said. "Our belief in him has not wavered."
In its official response Monday, the organization said it continues to deny tampering with the balls but was willing to face any discipline handed down. But the team and Robert Kraft, Patriots chairman and CEO, said the sanctions announced by the NFL "far exceeded any reasonable expectation."
Later in the week, an attorney for the Patriots published an extensive online rebuttal
of the NFL's finding in the case.
The rebuttal by Daniel L. Goldberg asserts, among other things, that the NFL's report inappropriately dismissed scientific explanations as to why Patriots' footballs would have naturally lost air during the January 18 AFC Championship Game
against the Indianapolis Colts. The Patriots beat the Colts 45-7 en route to a Super Bowl XLIX victory.
Investigation: 'More probable than not' that Brady knew
In the 243-page Wells report
, investigators admit there is less direct evidence linking Brady to tampering with the air pressure in the balls.
And no one says in the report that the quarterback tampered with the balls himself.
"We nevertheless believe, based on the totality of the evidence, that it is more probable than not that Brady was at least generally aware of the inappropriate activities of McNally and Jastremski involving the release of air from Patriots game balls," the report says.
The report includes phone records, texts and emails, including some exchanges between Brady and Jastremski
There are also text messages between McNally and Jastremski that include references to Brady and air pressure. And the report says it unlikely two employees would deflate any football "without Brady's knowledge and approval."
But Brady, who answered questions from investigators over the course of one day, did not turn over personal information such as texts and emails. That's something the NFL said it took into account when it decided on an appropriate punishment.
Yee told CNN's Anderson Cooper that the quarterback didn't agree to hand over text messages because that would set a bad precedent for other players involved in disciplinary investigations.
The online rebuttal written by Goldberg, the Patriots' attorney, asserts that McNally's and Jastremski's texts display nothing more than attempts at humor, and that the Wells report misinterprets them as references to a plot to deflate footballs.
'Protecting the integrity of the game'
In a letter to Brady, NFL Executive President Troy Vincent said the quarterback's actions were detrimental to the integrity of the sport.
"Each player, no matter how accomplished and otherwise respected, has an obligation to comply with the rules and must be held accountable for his actions when those rules are violated and the public's confidence in the game is called into question," Vincent wrote.
As it stands, Brady will be suspended for the first four regular season games of 2015 but can participate in training camp and other activities, including preseason games.
Jastremski and McNally, who have been indefinitely suspended without pay since May 6, cannot be reinstated without NFL approval, the league said.
If the men are reinstated, they will be prohibited from certain duties, such as managing the locker room or overseeing preparation of the game footballs.
Goodell said the punishment is in line with the findings of the report.
"We relied on the critical importance of protecting the integrity of the game and the thoroughness and independence of the Wells report," he said.