Middlesbrough are currently pursuing the services of Rhodes and after having their initial £12million bid for the Scotland international rejected, it was believed that Boro would agree to match Blackburn's reported demands of £14million.
However in an unexpected blow for the Teessiders, Blackburn boss Bowyer has revealed that the club owners have decided to increase their valuation of Rhodes.
Bowyer said: "Every player has a price, of course. But our owners are very good in the sense that if it's not met, they don't leave.
"It (the asking price) has changed. It changes a couple of times over the course of negotiations."