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Millen has refused to give up on securing Palace's permanent managerial post, but Newcastle boss Pardew continues to thrash out personal terms with Parish.
Millen believes Palace must avoid any repeat of the delays securing Neil Warnock as Tony Pulis' successor in August, when the club had to relinquish interest in Malky Mackay.
Cardiff owner Vincent Tan's complaints sparked the Football Association investigation into racist texts that cost Iain Moody the sporting director's role at Palace, and put paid to any chance of the Eagles recruiting Mackay.
"You'd think that it would cause a lot of unrest among the players, but they have coped unbelievably well," Millen said.
"When I've done this before it's dragged on for a few weeks, and that starts having an effect on the group, the not knowing.
"This has only just happened, with Neil leaving on Saturday, and the speculation today (Tuesday).
"So we've had one game and the lads were terrific in that (Sunday's 0-0 draw at QPR).
"But you wouldn't want it to continue for weeks on end, because that's when I think the lads want some guidance on where the club's going.
"So hopefully this can get solved pretty quickly."
Cardiff owner Tan's FA complaints over former Bluebirds boss Mackay forced Palace to start their summer managerial search from scratch, Warnock eventually coming out of retirement.
The former Sheffield United boss was sacked on December 27 after a run of just one win in 12 matches, and Millen admits stability will now prove crucial to Palace's chances of avoiding Premier League relegation.
Newcastle granted Pardew permission to speak to Palace on Monday night after the Croydon club agreed a compensation package with the St James' Park hierarchy.
Pardew is expected to double his salary in securing a move back to the club he served as a midfielder between 1987 and 1991.
Millen admitted Pardew has plenty of the credentials to impress at Selhurst Park, but continued to press his own case.
The former Bristol City boss said he still aims to return to management in future, but vowed to stay on with the Eagles if wanted by the eventual new boss.
"Alan's played for this club, he's from this area, he's got a lot of fond memories and it means a lot to him, this club," Millen said.
"Crystal Palace is a good job for somebody, I know it is.
"We've got a good group of players, we had a good season last year, and the chairman and the board want to build on what success we've had.
"So it's an attractive job and I can understand why Alan would be interested.
"I want to manage again, without a doubt.
"But I'm patient at the moment because I enjoy working at Crystal Palace.
"I enjoy my role working with the players, because they are a good group to work with and I come into work enjoying what I'm doing.
"You can't always pick and choose when jobs become available.
"I'm always on the look to see what's going on.
"I've had no approaches for a job so I've not had to make that decision, and I'm actively not looking for another job.
"At the moment I'm happy, and if a new manager comes in and sees me as playing a key role..
as long as someone comes in, sees what you're about and values what you do, then I'll be happy.
"And we'll see what happens in the future."
Source : PA
Source: PA