"We will approach it in whatever manner his family", he confirmed to the Associated Press, "however they would like it to be handled".
As they drove around Los Angeles, the Hollywood star, 48, said: "It was the first time we met".
The rock band are thought to have filmed the segment for the late night talk show just days before Chester died on July 20.
The show debuted Tuesday with an episode featuring Corden getting jiggy with Will Smith, though no air date has been announced so far for the Linkin Park ride-along, which was originally set to debut in October.
Conceived by Late Late Show host James Corden as a popular segment on that series, Carpool Karaoke premiered as a standalone spin-off on Apple Music Aug. 8, with plans to release a pair of episodes each week.
James is dropping the basketball and picking up a microphone to passionately sing "Maniac" with no one other than "Carpool Karaoke" host, James Corden.
According to Entertainment Tonight, Bennington and his band teamed up with funnyman Ken Jeong for the July 14 filming of the upcoming Apple Music series.
James confirmed that he gathered the rock group together in his vehicle for the viral segment and noted that it will now be up to Charles's family to decide whether or not it will air on The Late Late Show. "It's thrilling to me, you know?"
After this rendition of classic 1990's fare from Will Smith, fans can look forward to "Game of Thrones" stars Maisie Williams and Sophie Turner as they belt out "Wrecking Ball". "What a genius. What a guy", said Corden. It featured Corden and actor-rapper Will Smith.