Carver is in interim charge while Newcastle find a replacement for Alan Pardew, who was released from his contract on Saturday to take over at Premier League rivals Crystal Palace.
The 49-year-old oversaw a 1-0 defeat at Leicester City in the FA Cup third round on Saturday in his first official game as caretaker, two days after taking the reins for a 3-3 draw with Burnley as Pardew held discussions with Palace.
Carver is keen to take over on a permanent basis, but Newcastle are reported to have drawn up a shortlist of candidates thought to include former Lyon boss Remi Garde, Saint-Etienne coach Christophe Galtier and Thomas Tuchel, whose spell with Mainz ended in May.
Regardless of who is eventually appointed as Pardew's successor, Carver wants the situation to be resolved as soon as possible.
"Something has to be resolved sooner rather than later, it can't linger on," Carver said.
"So, whether it's with me or with somebody else, it has to be done quickly."
Carver faced criticism for resting some of Newcastle's senior squad members against Leicester, but he has been quick to defend a team selection apparently designed to protect players carrying injuries.
"When players come in you have to trust them," Carver added. "When they say to me they are injured, I have to take that at face value.
"It would help me if I put Moussa Sissoko, Fabricio Coloccini or Ayoze Perez on the pitch.
"But we could have lost them to injury because they were being put at risk.
"It would have helped my case to get the head coach job. So why wouldn't I put them on the pitch?
"It is in my best interests to put them out there.
"But it's taken out of your hands sometimes because of the injury situation.
"The only one who wasn't injured was Ayoze Perez."
