Mitchell started the search for a new boss earlier this week after the club parted company with Paul Groves and Shaun Books, and revealed the search was in full swing.
“The interest has been quite considerable and it has been a very intense few days,” he told afcb.co.uk.
“I've met a couple of people. I can't say who and I can't give you my thoughts on them.
“I've got an opportunity to find someone to help us succeed in what we want to do, and I have to be sure I've got the right person.
“He has to be determined, he has to be strong and he has to play football in the right way. He has to please the fans by getting results and looking after the young lads that we have got coming through.”
Mitchell also explained that the Cherries may be forced to seek permission to speak to managers already in employment to find the right man for the job.
“I think there is every possibility that we could end up approaching a club for someone who is currently in work but we'll have to wait and see,” he said.
“There have been managers that have caught my eye over the last few years and I would not rule out taking that route.”
Mitchell added that he was yet to hear from Groves and Brooks about whether they would accept an offer to take up positions in the youth set-up at the Goldsands Stadium.
“They want time to gather their thoughts,” he said. “I think they will probably wait to see who we appoint then make their decision, which is the wise thing to do.”