The Daily Mail says talks have kicked off between Rose and Cherries chief Tiago Pinto with the aim for a swift agreement.
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Current manager Andoni Iraola has announced he will leave Dean Court this summer when his deal expires.
Ipswich Town boss Kieran McKenna is also being considered, though Rose's free agency status makes him the preferred option.
Rose's high-pressing style is also seen as a good fit for the current squad as it is similar to Iraola's style of play.
Rose, 49, has been out of work since being dismissed by RB Leipzig a year ago.