Bowyer has been given the managerial position at Ewood Park on a permanent basis after filling in as caretaker boss for the second time this season.
And the new manager believes he has the complete backing of the board as he looks to keep hold of his prized assets - including Rhodes, who scored 27 goals last season.
When asked whether keeping Rhodes at the club was a priority this summer, Bowyer answered: "Very much so. I'm not talking about letting him go.
"I think the figures that people talk about, I don't entertain it at the moment.
"He was fantastic for this football club last season and we're wanting to build a team around him and reproduce what he did last season and be better. We'll be setting him that target.
"He got pipped at the post by Glenn Murray as the top goalscorer in the division, and we want him to be top goalscorer next season. Hopefully that then fires us to promotion."
Bowyer also made it clear that Blackburn will look to be competitive in the transfer market this summer.
"I've not been told that we have to sell anybody, that's been perfectly clear," he added.
"I'm aware that we're making funds available to sign people already, like we have done. We'll be competitive in the market.
"I don't think there's any pressure to reduce the wage bill. Obviously with the financial fair play there's a lot of talk about that at the moment so that's something we have to look at, but there's no indication to say you must reduce the wage bill by a certain amount.
"But I'm fully aware of the fact that one or two players might want to leave. If that's the case then we would have to strike the best deal for the club."