The Pakistan Cricket Board (PCB) was initially one of three countries which opposed the revamp of the International Cricket Council (ICC) approved by members in February.
The move handed the majority of the powers and revenues to the "big three" of the game -- India, Australia and England.
Pakistan and Sri Lanka abstained from voting on the reforms, but since then Sri Lanka have hinted they will sign the draft.
Sethi, who will attend the ICC meeting in Dubai on April 9-10, said Pakistan were offered a seat at the table but declined.
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"In the cricketing scenario, currently there are eight countries at one side and Pakistan at the other. The ICC doesn't need Pakistan after the rejection of such a rare offer."
Reacting to the claims, Ashraf confirmed an offer was floated at one stage but said it was never a firm commitment.
"They did offer us to join the group but when I went to attend the ICC meeting in February India stepped back from its offer, claiming two other members of the body -- Australia and England -- are not ready to admit Pakistan as a fourth member," he said.