The former RB Leipzig and Borussia Dortmund coach will take charge at the end of the season when Andoni Iraola will step down as Bournemouth manager.
Rose, reports BBC Sport, was one of three candidates considered by Bournemouth, alongside Ipswich manager Kieran McKenna and Rayo Vallecano coach Inigo Perez, who was Iraola's No2 at Rayo.
Asked about Rose, Iraola told BBC Sport: "I know him but I cannot speak about other managers.
"Because I speak with the club, I have some information. I've heard names but it's a decision that they have to make.
"And, whoever they decide, whenever they decide to sign the new manager, you can ask me about whoever comes and I will try to give my opinion."
Rose has been out of work since his sacking by RB Leipzig in March 2025.