Martin O'Neill has revealed that the Parkhead club will not be signing Portugese international Dani.
Dani will not be signing for Celtic
The club and player have failed to thrash out an agreement over a contract although O'Neill hinted that the deal may not be completely dead.
And the Celtic boss stressed that the invitation to former Barcelona midfielder Ivan de la Pena to return to Glasgow and prove himself worthy of a deal still stands.
Dani has spent the last few weeks training with the SPL club and appeared to have impressed sufficiently to be offered a deal.
He was invited to extend his trial period after O'Neill claimed he needed longer to assess the player because he was still short of fitness.
But the Parkhead boss admits Dani's fitness remains a problem and did not help the negotiations.
O'Neill told the club's official website: "We were delighted that Dani decided to come over here to train with us, and unfortunately at the end of it all we have been unable to agree any contract.
"He was over for a fitness assessment, but he has obviously been out of the game for a while and that didn't make things easier."
Striker Dani, who has been at Ajax, West Ham United and Sporting Lisbon, was not offered new terms by Atletico Madrid when his contract expired this summer.
But O'Neill insists the door is still open for Dani to make a return to Celtic in the future.
"Although nothing's happening for the moment, there's a possibility that this is something all parties concerned might revisit sometime in the future."
Meanwhile De la Pena's agent had claimed that the Spaniard was mulling over a contract offer and would not return for a second trial period.
The free agent, whose career began well at Barcelona before an ill-fated move to Lazio, has already spent a few days training with Celtic.
But the 26-year-old left to explore an offer to play in Qatar.
De la Pena rejected the move, paving the way for Celtic to renew their interest, but O'Neill appears unwilling to make an offer without another trial.
Ivan de la Pena has turned down an offer from Qatar
The Parkhead boss said: "I believe de la Pena is in Barcelona at the moment, but the offer for him to come back for some training in order that we can assess him a little further still stands.
"As yet, that's the extent of it, though. There's no contract on the table."
Both 26-year-old trialists had played for Celtic in a 3-2 closed-doors victory over Livingston at Airdrie's Excelsior Stadium.
De la Pena, nicknamed the Little Buddha when he broke through the ranks at Barcelona, saw his career falter after a move to Lazio and loan moves to Marseille and back to Barcelona were followed by a switch to Espanyol last season.
Some Celtic fans have criticised the club for failing to make signings before the Champions League deadline, but O'Neill stressed that he had not been made aware of the availability of de la Pena and Dani until a late stage.