Joshua started to work with Garcia and Angel Fernandez ahead of his rematch with Oleksandr Usyk on August 20 in Saudi Arabia.
Garcia is typically based in the USA but he relocated to England so he could train the British heavyweight.
He is now without a belt and has three losses on his record ahead of his comeback fight during the first few months of 2023.
The Brit is looking for a new trainer again and Garcia has advised him that he needs to have a "stricter camp" in future.
"Everything was kind of easy and quick for him," Garcia told Izquierdazo.
"He thought that that was the right way to do it, that he didn't need to do it in another way.
"When the time comes for this kind of fight with fighters of a higher level - tougher fights, harder fights - you need a stricter camp, where he follows indications.
"I feel that he is taking the decision about coming to the United States.
"If he came to talk with trainers such as Derrick James, who is very busy here in the United States, I don't think that AJ's plan is to take him to Europe. Maybe [Joshua] is planning to stay here.
"I will be happy to see him here, even if he is not working with me. AJ needs a change, a completely new change to what he is not used to."
Garcia is certainly onto something here. Him relocating to England to train Joshua felt bizarre at the time and the heavyweight could have benefitted from getting out of his comfort zone during his camp for the Usyk rematch.
His promoter - Eddie Hearn - has confirmed that he will take on a top 15-ranked heavyweight next. If he wins, he is then likely to battle Dillian Whyte or Deontay Wilder in a mega fight in the summer.