Carver is desperate to be handed the job full-time and take the club to European success like Joe Harvey back in 1969.
Unconfirmed reports claim the club have opened talks with Frenchman Remi Garde with a view to succeeding Alan Pardew as head coach.
But Carver is adamant he has what it takes to match Pardew's best season at St James's Park when he led the Magpies to a fifth-placed finish in 2012.
Carver said: "The fact I have put my hat in the ring, some people will say I was crazy - but I want to do it.
"We finished fifth a couple of years ago and that was fantastic - so why can't we push fifth, sixth, seventh, eighth?
"There's all this talk that the club is happy to sit in the top 10. But no - set your marker as high as you can and if you can get there then what an achievement.
"We've proved we're capable of that when we had our recent run of six wins on the bounce."
Carver's caretaker reign did not get off to the best of starts when he dropped big names including Moussa Sissoko, Daryl Janmaat and Fabricio Coloccini for last week's FA Cup defeat at Leicester.
The weakened line-up provoked a furious response from Magpies fans but Carver insisted he had no choice but to make seven changes to his squad due to a series of niggling injuries.
Carver added: "That's the unfortunate thing about being caretaker-manager - you are on interview all the time.
"It's a bit unfortunate because normally a new manager is given time to put his ways across.
"I know the pitfalls and what comes with it. It hasn't been a great few days. But I love it. I still want to do it and I have the drive and enthusiasm to do it."