The fire occurred a day after plans to remove Koffa from his speaker role sparked a tense protest.
Several demonstrators, including an aide to former President George Weah, were arrested during Tuesday’s protest.
Representative Foko, a prominent figure in the House of Representatives, allegedly uploaded a video onto Facebook in which he said: “If they want us to burn the chambers, we will burn it.”
Police chief Coleman said: “Representative Foko made a threat that he would burn the joint Chambers and just a day after, it was burned. So he needs to clarify his statement.”
Coleman said Koffa must also explain a Facebook post he made during the protests.
Neither Foko or Koffa have responded publicly to Coleman’s comments.
The government has offered a $5,000 (£3,900) reward for more information about the fire.
President Joseph Boakai has expressed disappointment over the incident and ordered the security agencies to investigate.
Liberia’s House of Representatives has been beset by a power struggle, in which a faction of lawmakers claims to have removed and replaced Speaker Koffa.
Another group has resisted the action, calling it unconstitutional.
A Supreme Court ruling has failed to solve the internal dispute.
