The Cherries have made a flying start to the new League Two season, winning five of their first six games to leave them joint top of the table.
They have done so using a skeleton squad, with manager Eddie Howe unable to add any extra numbers owing to the embargo which was placed on the club after its previous owners ran into financial difficulties.
But Mitchell, who heads up the Murry Group that now runs the club, wants more fans to come through the turnstiles to help rid the club of its problems.
"The board is hoping that we can get the embargo taken down a level by paying the football creditors," he told Bournemouth's official website. "This would bring the club a step closer to bringing in loan players.
"Things are very slowly being put right. There is however, a long way to go, so let us set a target of over 6000 seats for our next home game."