(CNN) House Intelligence Chairman Adam Schiff told CNN on Thursday that his committee has no plans to hear testimony from former national security adviser John Bolton before President Donald Trump's impeachment trial in the Senate, arguing there's "little to be gained" by going that route at this moment.

Schiff, a California Democrat, said "we have not" had discussions with Bolton or his team since the former White House aide announced this week that he'd be willing to testify before the Senate if subpoenaed.

With Republican senators resisting calls to bring him in before their chamber, some have suggested that House Democrats should instead compel testimony from Bolton, who previously warned the House Intelligence Committee he'd fight any subpoena in court.

But Schiff said Thursday that Bolton should testify before the Senate -- not the House.

"We haven't taken anything off the table," Schiff said, leaving a meeting in House Speaker Nancy Pelosi's office. "But if we are proceeding in a rationale way where we are trying to be fair to the President and fair to the American people, he should testify before the triers of fact, which are the senators."

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