Rhodes was strongly linked with a move to in the transfer window.
“Jordan is not unhappy. You don’t work as hard as he did against Bolton on Saturday and score twice if you’re unhappy,” Bowyer 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.”
The 23-year-old joined Blackburn in a £8million deal from Huddersfield Town last summer.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.