Matthew Maynard has told the BBC's Sport Wales programme it looks highly unlikely that Jason Gillespie will be allowed to join Glamorgan this season.
Maynard, the county's cricket manager, has been waiting in vain for a decision from the England and Wales Cricket Board on the Australian's registration.
This is due to an issue with him potentially joining the rebel Indian Cricket League (ICL).
When asked if the deal could fall through, Maynard said "That's correct."
The ICL is in direct opposition to the International Cricket Council-backed Indian Premier League (IPL).
Governing bodies have threatened to ban ICL players from first-class cricket, but Glamorgan hoped Cricket Australia would grant Gillespie an exemption so that his possible spell in the ICL will not jeopardise his contract in Wales.
"A couple of weeks ago, I spoke to David Collier, the chief executive of the ECB, about a letter I had received from Cricket Australia which I was led to believe was a no objection certificate," Maynard told Sport Wales.
"Every county who has an overseas player in the ICL has to have a no objection certificate from their relevant boards.
"I received a letter from Cricket Australia but I don't believe it is worded strongly enough to be a no objection certificate.
"The ECB have asked for a certificate but that, at this stage, has not been forthcoming.
"We've sent off all the registration forms and hopefully we'll hear by the end of this week or Tuesday or Wednesday of next week whether they will sign off his registration to play as an overseas player for Glamorgan.
"It's up to the ECB whether they accept and sign the registration but Cricket Australia hold the key.
"If they don't issue a no objection certificate, there's nothing we can do."
If Gillespie does eventually arrive at Sophia Gardens he will be Glamorgan's fourth signing of the winter, following batsman Matthew Wood, bowler Adam Shantry and England all-rounder Jamie Dalrymple to Wales.
Gillespie, 32, has taken 259 wickets in 71 Tests, making him Australia's fifth highest wicket-taker.