The 47-year-old assumed temporary control at Selhurst Park on Friday after Tony Pulis left the club by mutual consent 24 hours earlier.
Millen was unable to guide Palace to victory on the opening day of the Premier League season, as Arsenal came from behind to win 2-1 at the Emirates Stadium with Aaron Ramsey scoring a late winner after Brede Hangeland had put the visitors in front.
Speaking after the defeat, Millen admitted becoming Pulis' permanent successor would interest him but will speak to co-chairman Steve Parish on Sunday before throwing his hat in the ring.
"I'd like to continue, I enjoy being in charge," said Millen in his post-match media conference. "Whether it's the right time or not [I don't know].
"I'll speak to the chairman tomorrow.
"It's been very quick in the last two days, the chairman's not had a chance to talk to the players, to talk to me about his ideas going forward, we just focused on today's game.
"On Monday I'm sure there will be more conversations because the players need to know what direction the club wants to go in and hopefully at the start of the week there will be some more answers."
Despite Palace's defeat, the caretaker manager was full of praise for his players.
"I am proud of the players, proud of the performance," he continued. "But disappointed not to have got something out of the game which I think we deserved, and more disappointed with the manner of the goals we conceded.
"The players can take a lot of confidence from their performance, we know we can compete at this level, we know we've got to get more competition for places, but the players are waiting to be given a new direction on and off the field."
As well as conceding two goals Palace also had Jason Puncheon sent off in the closing minutes for two bookable offences, a decision Millen felt was harsh on the winger.
"The first one [tackle] was a yellow card," he admitted, "But the second there's minimal contact to be fair, I didn't see it as a booking to send him off."
