The comment was made by Abbott during an interview on a conservative talk radio show on Wednesday.
Abbott says Texas may "resurrect" the case of Plyler v. Doe from 1982.
The ruling gave all children the right to free public education, including the kids of undocumented immigrants.
Critics have already called the idea 'alarming' after the leaked Supreme Court draft opinion on Roe v. Wade.
"Texas already long ago sued the federal government about having to incur the costs of the education program, in a case called Plyler versus Doe," Abbott said. "And the Supreme Court ruled against us on the issue. I think we will resurrect that case and challenge this issue again, because the expenses are extraordinary. And the times are different than when Plyler versus Doe was issued many decades ago."
What is Plyler v. Doe?
In 1975, Texas changed its education laws to deny enrollment to children who were not "legally admitted" into the country, and to withhold state funds for their education.
In 1982, by a 5-4 vote, the Supreme Court ruled that the Texas legislation violated the Equal Protection Clause of the 14th Amendment.
The Supreme Court said, "Education has a fundamental role in maintaining the fabric of our society" and "provides the basic tools by which individuals might lead economically productive lives to the benefit of us all."
It also stated that there was no evidence that removing undocumented children from the school system would improve the quality of education in Texas.