"Let's not put carts before horses," the two-term governor told reporters in Washington, where he was trying to rally support for a possible bid for the GOP presidential nomination.
"We have a month to go, so let's see what happens," Kasich said, adding that he'll announce whether he's running on July 21.
The first confrontation between GOP hopefuls, set for Aug. 6, is to take place in Kasich's own state. Debate organizers at Fox News Channel, backed by the Republican National Committee, have limited the debate to the top 10 candidates in national polling.
Trump would qualify under those terms, while Kasich would not.
The billionaire New York developer and reality TV star has dominated the news with his description of Mexican immigrants as criminals and rapists. Many Republican officials have condemned those remarks, but Trump has not backed down.
Republican donor John Jordan said Monday that GOP leaders should take steps to block Trump's access to the debate.