The Professional Rugby Agreement (PRA) - a key priority for Tierney since her appointment in January 2024 - has been delayed by 12 months of negotiations.
Sticking points are thought to have included the extent of the WRU's say on national players, including when they play regional rugby and potentially which side they play for.
A breakthrough in February appeared to ensure four regions would be maintained and also that there would be extra funding.
But it has emerged that Cardiff's inability to commit to a three-year funding plan because of the absence of investment from new backers Helford Capital Ltd also hampered the process.
Dragons, Ospreys and Scarlets are now seeking clarity from the WRU over what this week's events at Cardiff mean to the agreement and their future relationship.
"We were so close [to a deal]. We had really good conversations with all four regional boards, including the previous Cardiff board, who had all agreed a deal in principle," Tierney told the Scrum V podcast.
"Cardiff has caused challenges this week but we've had really positive conversations with the other three CEOs [chief executives] and they have questions, but we're within touching distance. We're determined we'll get it over the line."
Tierney said the WRU was aware of financial issues at Cardiff back in September and among the club's debts was £9m owed to the governing body.
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