The 23-year-old Australian headed home to his family in Melbourne yesterday after discussions with the Parkhead managing director Fergus McCann, his advisors IMG and his former club Croatia Zagreb.
Viduka is not expected to return to Scotland until the new year after fleeing to Zagreb on Sunday, complaining of depression just five days after joining the reigning champions.
The complicated payment of his pounds 3m transfer fee - understood to include a substantial figure to the player - appears to remain unresolved, with McCann asking for Fifa assistance in the matter.
McCann and Eric Riley, Celtic's financial director, are believed to favour an agreement that withholds the payment due to Viduka pending his return, while Zagreb are expecting their instalment by the end of the week.
In a joint statement by the player and McCann last night, Viduka pleaded for sympathy for his plight and vehemently denied his actions were linked in any way to the alleged financial shortfall to him.
"Of course I regret that my intention to play for Celtic has not yet been fulfilled," he said. "I do appreciate the club's understanding. All I want right now is to be left alone to recover from the stress of my last few months in Zagreb.
"I want to play football again soon, and when I am ready, I want it to be for Celtic. I want to make it absolutely clear that as far as I am concerned this is not about money. My only concern is getting back to total fitness and honouring my commitments. I hope people realise that I have been honest and up front, I am not the sort of guy to try and hide my feelings."
McCann, who flew to Zagreb yesterday in an attempt to rescue his investment in Viduka, declared himself satisfied with the agreement reached over the player in his present state of unfitness.
"The Zagreb officials recognised that the purpose of the transfer - for Celtic to obtain the player, ready, willing and able to play - had not been achieved," he said. "We are hopeful that with their understanding and co-operation, the matter can be resolved effectively and amicably.
"We also hope that the assistance and advice of the football bodies, principally Fifa, will be available to deal with this situation fairly, as necessary. The player and his representatives have been very co-operative and we appreciate his difficult position."
Whether that involves the full transfer of Viduka's fee at the present time remains unclear, although a Zagreb spokesman, Goran Bradic, earlier confirmed that his club are expecting an instalment in the next few days.
"We are expecting payment from Celtic at the end of this week," he said. "We were never worried because the law is on our side. Celtic must pay and they said they will."
Meanwhile, the Scotland striker Ally McCoist last night accused Aberdeen's under-achievers of failing their former manager, after Alex Miller became the latest man to vacate the Pittodrie job.
The Kilmarnock player laid the blame for Miller's demise firmly at the feet of the Aberdeen players, after learning that Craig Brown's Scotland No 2 was on his way out of the door after barely a year in the job.
McCoist and his team-mates helped seal Miller's fate on Saturday by humbling woeful Aberdeen 4-0 at Rugby Park.
"It was a poor performance on Saturday and they haven't been playing very well at all lately," said McCoist.
"But the players have got to take a good look at themselves because they have really underachieved for the last few years. They have some real quality players up there and they should be doing better than they are."