Mitchell's comments come after boss Lee Bradbury offered new deals to six out-of-contract players Stevie Lovell, Danny Hollands, Mathieu Baudry, Ben Williamson, Dan Thomas and Tim Stephenson.
While Baudry, Williamson, Thomas and Stephenson have already indicated they are likely to agree terms, Lovell and Hollands are still weighing up their options.
Lovell, who drew only 50 per cent of his salary for much of an injury-ravaged season, has so far remained tight-lipped on his future plans after being offered a one-year deal with a 12-month option.
And although Hollands, who has been tempted with a two-year contract, has already publicly stated his desire to stay, a number of other clubs including League One champions Brighton are believed to be on his trail.
Bradbury is this week hoping to hear from Lovell and Hollands, two of the club's higher earners, with their decisions likely to impact on the make-up of his squad for next season.
Cherries also need to agree a suitable compensation package with representatives of the Glenn Hoddle Academy before Williamson can commit to his one-year deal with a 12-month option.
Mitchell told the Daily Echo: We want to keep the squad together as much as we can but are not going to break the bank to do it. We know exactly what we have got to offer and I think we are an attractive proposition to people. We have a cap on wages and that will not be broken.
When you look at someone like Marvin Bartley, you have to ask what the point of moving was other than the extra money because he has hardly featured at Burnley.
Mitchell and the Dean Court board backed former boss Eddie Howe in the transfer market following Cherries' promotion last season when no fewer than eight new signings were drafted in.
Asked whether Bradbury would be given scope to manoeuvre in the summer, Mitchell replied: We have got players fighting for places so I don't think the squad needs strengthening that much.
But we need a few fresh faces, every club does. We are in the market place to buy. We don't want to lose the momentum next season.
Meanwhile, Bradbury has quashed rumours on social networking site Twitter linking him with a move for Exeter City defender Matt Taylor.