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"They should go wherever the facts lead. They may be able to get what they want and need without him testifying," the South Carolina Democrat told CNN's Dana Bash on "State of the Union." "I would not want to see a former president testify in such a situation as this, but if that's what it takes in order to get to the bottom of this."
Thompson told CNN following his appointment that he "would not resist" calling Trump to testify if the information they gathered led to him.
"I would not, if prompted, say that we should do it, but I would not resist it if we went there," Thompson said.
Thompson made clear that GOP members of Congress and Trump White House officials are not off limits as well.
"Well, I think we need to have access to all the available information. And part of what we plan to do is hire some of the best people, who can help us get access to that kind of information. So, if we need to get it by request or by subpoena I'm not reluctant to do either," Thompson said.
McCarthy has not yet announced his Republican appointments to the committee.