Fraser has been given a week by Blues hierarchy to decide if wants to bid for the permanent position.
Fraser has softened his previous stance of ruling himself out of vying for the fulltime job, despite reviving Carlton's fortunes with eight wins and two losses since replacing Michael Voss.
"It's not so much umming and aahing, I think it's just considering everything that comes with being a senior coach and being prepared to go through that process," Fraser told reporters on Thursday.
"And I have got a high awareness of it and this (interim) opportunity has given me a chance to live it to a degree.
"But I want to make sure that if I go through a process, if I was to be successful, that I am ready to hit the ground running."
Carlton's football boss Chris Davies earlier Thursday said the club was in the second phase of finding its next fulltime coach.
"It's fair and reasonable to say that after 10 weeks, he (Fraser) has a better understanding of where he's at ... we think he should put his hand up," Davies told SEN radio.
Current assistant coaches Jaymie Graham (Fremantle), Corey Enright (St Kilda) and James Kelly (Geelong) are other candidates.
"I'm going to be careful in not confirming who's in or out of our process," Davies said.
He expected a decision by the end of the home-and-away season, which concludes on August 23 as Fraser weighed up his desire to one day be a head coach with his fit for the Carlton vacancy.
"I'm ambitious, and I have been, to be a senior coach," Fraser said.
"No doubt that the excitement has probably been fast-tracked by this interim opportunity.
"But right through my coaching journey I have been very considered with what I have done and how I have done it, and I have always wanted to consolidate each role I am in."
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