Hull have been on the hunt for a new striker since selling Shane Long to Southampton in a reported £12 million deal earlier this month, and they appear to have identified a potential replacement.
Bowyer, whose side host Bournemouth on Saturday, said: "There has been an enquiry which has been taken to the board and the owners and that's as much as I know."
Rhodes, capped 11 times by his country, has a prolific goalscoring record and has netted more than 20 goals in each of the last five seasons.
That form has put him firmly on the radar of Premier League scouts, but the 24-year-old penned a new five-year contract at Ewood Park in July.
Hull, who lost new signing Robert Snodgrass to a long-term injury this week, are in Europa League action against Lokeren on Thursday.
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