Eddie Howe's heroes have enhanced their reputations by helping the club achieve an against-the-odds promotion from League Two this term.
The team's fine form in likely to have alerted the scouts with top scorer Brett Pitman rumoured to have caught the eye while highly-rated boss Howe's exploits have also unsurprisingly attracted plenty of attention.
Experienced manager Micky Adams, whose Port Vale side were on the receiving end of a Dean Court drubbing on Saturday, said he felt Howe could emerge as a top target for Championships clubs.
But Mitchell insists he does not want to sell and is focused on helping provide his manager with the best possible opportunity of succeeding in the third tier.
He told the Echo: The boys have done fantastically. I'm sure there will be people trying to prise one or two out of us and I think probably one or two trying to prise the managerial staff out of us. But at this moment in time, we're not selling.
The club has always been a selling club. But we want to stabilise the club and not sell our best assets. We think we can take them further.
It wouldn't be right to keep people back who can propel themselves further up the divisions, such as Brett perhaps. But by and large they are a young squad and there is plenty of time for that to happen.
I think Eddie is the best guy to teach them how to get further up the ladder and when they are a bit further on, we might release them to go further. But at the moment, they are contracted and they are staying.
Since Mitchell took control, Cherries have demonstrated a desire to retain the services of their leading lights by handing extended deals to the likes of Pitman, captain Jason Pearce and goalkeeper Shwan Jalal.
Meanwhile, Mitchell was quick to stress that the club's board had hard work ahead of them during the close season. He highlighted two major hurdles an insolvency payment (often incorrectly referred to as a CVA) and bringing the stadium rent up to date that needed to be overcome.
The Dean Court chief added: The board are not going to be out there jollying and forgetting what there is still to clear.
Mitchell also wished to thank an anonymous fan who donated £500 to the club at Saturday's game.