The former Crystal Palace manager took over at the start of the month and won on his home debut against Ipswich Town on Saturday.
"I'd like to be here longer than six years. I can't say that now because they might not like me. But everything I value and have been brought up with, [chairman] John [Berylson] carries it in his heart and we are on the same page," the Daily Star quotes Holloway as saying.
"What I'm trying to say is please join me on my journey. I want it to be the best trip we've ever been on."
Millwall are 20th in the Championship.