Irving was heavily criticized for promoting a film that the seven-time All-Star has since said contained "false anti-Semitic statements".
The Nets suspended him for at least five games after he "refused to unequivocally say he has no anti-Semitic beliefs".
Irving later apologized to those "hurt from the hateful remarks made in the documentary".
"Based on what he said directly, to me (I) have no doubt that he's not anti-Semitic but I think there's a process that he's going to now need to go through," Silver said in Washington on Thursday, according to the website.
Silver, who is Jewish, told the New York Times he had a "direct and candid conversation" with Irving.
"He's someone I've known for a decade, and I've never heard an anti-Semitic word from him or, frankly, hate directed at any group," he said.
Silver added: "Whether or not he is anti-Semitic is not relevant to the damage caused by the posting of hateful content."
In addition to the suspension, Brooklyn outlined a list of six requirements he had to fulfill before rejoining the team.
They included apologizing, condemning the film, making a $500,000 donation to anti-hate causes and completing anti-Semitism training.
Irving's former team mate LeBron James said that while he did not believe in sharing "hurtful information," Irving should be allowed to return to the court following his apology.
"Help him learn - but he should be playing," James tweeted on Thursday.
"What he's asked to do to get back on the floor I think is excessive IMO. He's not the person that's being portrayed of him."
If he serves a five-game suspension, Irving would be available to play on November 13th against the Lakers in Los Angeles.
