Canseco and his girlfriend had just bought the goats and he was providing a running commentary during the trip home to Las Vegas. He asked how to stop the goats "head-butting" and said they were wearing diapers in case they urinated or defecated.
"Just got pulled over with goats in the car," he said in one tweet. "The cop laughed at our poor goats."
Canseco's girlfriend, model and talent agent Leila Knight, told the Toronto Star the goats are miniature silky fainting goats, which get their name by contracting their muscles and falling over when they are startled. She said the pair have been named, at least for the moment, Coco and Chanel.
"We bought fainting goats ... because we both love animals and he really wanted to get some goats," she said.
Knight answered Canseco's cellphone and told the Star he is only interested in paid interviews.
Canseco, born in Havana, was brought to the United States from Cuba as a baby. He played for 16 years in the major leagues for seven teams, with his longest stint seven years with the Oakland Athletics.
After his retirement, Canseco admitted using steroids and said 85 percent of major league players were also doing so.
Swim Week Miami Beach 2014 [PHOTOS]