The US international striker is currently training at Parkhead and manager Neil Lennon confirmed last week he would look at the possibility of signing the 19-year-old.
But his Los Angeles-based club don't want to sell Agudelo and have warned the SPL champs he's not for sale.
Chivas USA communications manager Rodrigo Ochoa said: "For us, the club, for the organisation, Juan Agudelo is just keeping fit training with Celtic, and that's it. There are no plans for the club to take any kind of transfer.
"He's taking advantage of the vacation time we have right now and he's training and keeping fit."
Celtic were hoping to take advantage of the fact his contract will finish at Chivas next year and they could lose him for nothing if they wait until then.
But Chivas – who are currently without a manager – will try and offer him a new deal to stave off interest from the Hoops.
The player himself – who also had trials at Liverpool and Stuttgart – admits he hasn't made his mind up yet about his future.
But he revealed last week he was enjoying his time in Glasgow.
Aguedelo travelled to Scotland fresh from starring for his country in a 2-2 draw against Russia in Krasnodar.
He is the youngest player ever to score for the USA, when he netted the only goal in a 1-0 win over South Africa.