The England and Wales Cricket Board said on Sunday Ireland are unlikely to be admitted to the National League until 2006 at the earliest. Ireland made a credible case to join Scotland in the competition with a convincing 10-wicket win over Zimbabwe in Belfast last Friday.
And captain Jason Molins, who scored an unbeaten century in the match, confirmed the National League was a target for his side.
"We want to test ourselves week-in and week-out and to do that we need to be playing National League cricket, just like Scotland," Molins said.
But the ECB said there were no immediate plans to rush Ireland into the one-day competition, adding that no formal application had yet been made by the Irish Cricket Union.
"The issue has not been brought up yet, though we are in regular contact with the ICU," John Carr, the ECB's director of cricket operations, told this website.
"When it was agreed to allow an associate member into the National League, it was done so on a three-year trial basis to be reviewed at the end of the 2005 season.
"The agreement was made for Scotland without consideration for any other team."
But Carr said the ECB was not inflexible on the matter and would give condideration to any advances from the ICU.
"If the ICU made a specific application and Scotland continued to perform well, then who knows?"
Molins believes Ireland need more regular competition for standards to rise further.
"For us to win with more than 15 overs to spare, and by 10 wickets, certainly puts a marker down that Ireland should be seriously considered by county sides.
"We are an amateur side and this is our first match all year - that puts things into context."
Ireland made a mockery of the supposed gulf in class between the two teams, by reaching their target of 183 in the 34th over.
It was the latest setback for the touring Zimbabweans, who suffered successive innings defeats in two Tests against England.
"I had my luck early on but we got a good partnership going and once we got used to the pace of the wicket were were able to win quite easily," said Molins.