Arsenal hero Wilshere is currently in charge on a caretaker basis after replacing Johannes Hoff Thorup following his dismissal a fortnight ago.
Stacey told BBC Radio: "We have complete trust in the board to pursue whoever they think is the best man for the job.
"Personally, and I think I can speak for all of the changing room, I think we'd be delighted for Jack to get it.
"You always want a manager that shows belief in you. The way he's come in and instilled confidence into individual players, it makes you want to do well for him and feel you can perform to your best."
The enjoyment is back
Stacey also admitted: "It can sound silly but for me it's about getting that enjoyment back into the football.
"Throughout my career I've played my best football because you feel free and can go onto the pitch and try things.
"It is about trying to get that freedom back and the positivity – I think the fans want to see it and maybe they saw a little more of it in the last game."