Newcastle confirmed on Saturday that Pardew, who was given permission to speak with Crystal Palace last Monday, had been released from his contract in order to take over at Selhurst Park.
Carver oversaw second game a caretaker manager in the FA Cup third round against Leicester City on Saturday as Newcastle tumbled out with a 1-0 defeat.
But despite that loss, the 49-year-old publicly announced his desire to take full-time charge of his hometown club.
"I'd just like to say now it's been announced Alan has taken the job [at Crystal Palace], I'd be a fool if I didn't want to be manager of this football club, or head coach," Carver said.
"Deep down inside I was always thinking that. I am putting my hat in the ring, I told the players that on the first morning, and now I'm making it public."
Should he get the job, Carver would be known as the head coach instead of manager, with Newcastle confirming the change in job title on the back of Pardew's exit.
That may indicate that Pardew's replacement will have no say in the club's transfer policy, but that is something Carver is comfortable with.
"I've not spoken to [owner] Mike [Ashley], my only communication has been with [the managing director] Lee Charnley," Carver added.
"We had a short conversation last night about the game today, nothing else, and that's been my contact.
"The only thing I will say is the position is now not manager, it's the head coach, and his job is to get the team ready for the next game. There's no need for me to be in touch with the owner, because that's the road the club is going down now.
"When I was head coach at Toronto FC I had a director of football, I never got involved in any transfer dealings, my sole responsibility was to get the team ready for the game, and I'm assuming that's what most head coaches do."
