The dispute began April 12 when Silverman asked that he and his two daughters be allowed into Municipal Stadium for the $6 discounted price even though he did not have a church bulletin.
He was told by a team employee that he would have to pay the full price of $8.
Silverman contends the promotion discriminates against him because he is an atheist.
Michael Berman, an attorney working on the case for Silverman and the ACLU, said the matter now can go to a public hearing before an administrative law judge. But he said the case could be resolved without further legal proceedings if the two sides could negotiate a settlement.
Berman said he has written a "very reasonable" proposal for a settlement but would not reveal its contents.
Suns' attorney Joseph A. Schwartz III said he anticipates a hearing will be needed to settle the matter.
"I think their negotiations are, 'My way or the highway,'" Schwartz said.
The Suns have maintained the promotion does not exclude anyone on the basis of religious conviction because church bulletins are widely available. Blenckstone said the team will continue to hold the promotion on the three Sunday home games remaining this season.
Schwartz likened Silverman's case to someone challenging a senior citizen discount because of age discrimination or claiming that a ladies' night promotion at a bar is a form of sex discrimination.
"This is the sort of nonsense that people say, 'This is crazy,'" he said.
Now in its fifth year, the promotion offers families of up to six people a group admission price of $6 with a church bulletin.
Silverman was charged the regular admission price of $5 plus $3 for one of his two children on April 12. The other child was admitted free because he was 4 years old, a Suns policy.
Meanwhile, the Suns are sponsoring a "Faith Community Night" on Aug. 17, when the team hosts the Macon Braves at 6:05 p.m. The team will use a portion of the gate receipts to help pay the team's legal bills in the matter.
Blenckstone said the evening also is a way of saying thanks to the community for the support the Suns has received.