The 23-year old has netted four times in his opening five Championship games this campaign having commanded an £8million fee to make the switch from Huddersfield Town last summer.
Rhodes' future has been surrounded with speculation throughout the summer with Wigan amongst the clubs interested, but Bowyer says the Scotland international is content at Ewood Park.
"Jordan is not unhappy. You don't work as hard as he did against Bolton on Saturday and score twice if you're unhappy," he told reporters.
"We're glad the window has closed now and all the speculation is over.
"Now I hope the lads come back fit from international duty and kick on."