Chairman Paul Russell says Glamorgan would seize any chance to return to the Twenty20 Cup if Yorkshire are expelled.
The Welsh side were knocked out in the group stages, but Yorkshire are under investigation for allegedly fielding an ineligible player against Notts.
Glam would be next in line to replace them, but a replay between Yorkshire and Notts, where spinner Azeem Rafiq, 17, played, is the most likely outcome.
"We would seize the chance with all the energy we could muster," said Russell.
"There must be a slim chance that we will get back into the tournament."
Durham's Twenty20 quarter-final with Yorkshire on Monday was remarkably postponed two hours before it was due to start.
Russell believes that although it was "a terrible shame" the match was postponed, the England and Wales Cricket Board made the right decision.
"It must have been an enormously hard decision," he said.
"But if the game had been played, the consequences could have been completely disastrous."
Russell admitted he felt pity for both Yorkshire and Durham.
"I have a huge amount of sympathy with Durham who are an entirely innocent party in all of this," he said.
"I don't think Yorkshire acted with any mendacity or ill purpose. I think it's a genuine oversight on their part."
Rafiq made his Yorkshire debut in their final group match against Notts.
It emerged that questions had been raised about Rafiq's British nationality and that he was only eligible to play at levels below the first team.
An ECB spokesman said: "ECB made it clear to both counties that in view of the alleged ineligibility of Azeem Rafiq, it was possible the panel could order the replay of any match or matches which could affect any quarter-final.
"The ECB are convening a meeting of the panel as a matter of urgency so that any relevant matches will be played before Twenty20 finals day at Southampton on 26 July," an ECB statement confirmed.
ECB chief executive David Collier announced that a meeting had been pencilled in for Thursday.
Yorkshire chief executive Stewart Regan told the BBC that the club's failure to register the player properly was his responsibility.
Durham say they should be advanced to the Twenty20 finals day.
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