The Eagles are set to step up the search for Ian Holloway's replacement next week, with former Stoke boss Tony Pulis understood to be high on the shortlist of co-chairman Steve Parish.
Millen made half a dozen changes to what was Holloway's final starting XI in the 4-1 home defeat by Fulham on Monday for the visit of Arsenal, and for large spells they caused the Barclays Premier League leaders plenty of concern before eventually going down 2-0.
However, the 47-year-old former Palace apprentice accepts the upcoming backroom changes could see him also eventually follow Holloway out of Selhurst Park.
"No I haven't (been given any guarantees). I have not really had that discussion with the chairman," he said.
"I was proud to be asked to take over the team against Arsenal and enjoyed it, so I think it will be a case of the chairman decides on who he wants top bring in and the next question will be 'do I fit into that?'
"I have been here before. I am experienced now. I know how football works.
"If I am asked, I would love to stay and work at this football club."
Millen added: "The most important thing for me is you trust the people you are working with and people know me well enough in the game to know I work with people and I trust them.
"That is how I would expect it to be if I was the manager."
Despite having now lost eight of their opening nine games back in the top flight and with a somewhat disjointed squad following so many new additions, Millen believes the south-east London outfit remain an attractive proposition for any coach.
"The owners that run this club from the top have got this club in a good situation. The fans are definitely with you, and I think you've got a talented group of players - it is just trying to get the balance of what is your best team," he said.
"The new manager will have to assess the group very quickly, but if he asks for my opinion I think he saw a team spirit and togetherness that would make most people want to come and work with them."
When Mikel Arteta had been sent off on 65 minutes for what was ruled a professional foul on former Arsenal striker Marouane Chamakh not long after scoring from the penalty spot, Palace rallied.
The final outcome could have been different but for a brilliant double save by Arsenal goalkeeper Wojciech Szczesny to first turn Joel Ward's 20-yard drive onto the crossbar and then palm away another goal-bound effort from Mile Jedinak.
Arsenal went on to secure all three points when Olivier Giroud headed in with three minutes left following a quick break.
Defender Ward said: "We just wanted a reaction and tried to give everything. I think we did that.
"It is tough, but you have to rise above it and take the positives from every game and try to build on what you can.
"Everyone has their own ways of doing things and whoever comes in, we will just adapt and move forward, then hopefully we can start picking up points where we can."