Rival protests have either called for Yoon’s impeachment to be declared invalid or for him to be detained immediately.
Yoon would become the first sitting South Korean president to be arrested if investigators are able to detain him.
His legal team have said they will not comply with the current warrant.
The Corruption Investigation Office (CIO) has declared it would “prepare thoroughly” for the second arrest attempt.
CIO chief Oh Dong-woon has apologised for the failed first arrest attempt, saying he was “heartbroken”.
PSS chief Park has twice ignored police requests to appear for questioning over allegations of obstruction of public duty since his team blocked investigators from arresting Yoon on January 3.
The PSS said Park could not leave his post due to “the serious nature” of protecting Yoon, but police warned they would consider an arrest warrant for the PSS chief if he failed to appear for questioning Friday.
“He appears to believe that he must avoid being arrested himself in order to better protect the president,” Shin Yul, a political science professor at Myongji University, told AFP.
Tense standoff
Meanwhile, Yoon’s guards have been increasing security at his central Seoul residential compound with barbed wire installations and bus barricades.
Yoon’s legal team said Friday the guards “remain on high alert 24/7” for another arrest attempt “despite immense pressure and stress”.
Separate from the insurrection probe, Yoon also faces ongoing impeachment proceedings — lawmakers have already suspended him, but the country’s Constitutional Court will decide whether to uphold this or restore him to office.