A prolific performer in the Football League, Rhodes continues to generate speculation suggesting he could soon be on his way to the Premier League.
He has, however, completed just one season at Ewood Park since making an £8million move from Huddersfield Town.
Rovers are understandably reluctant to part with the Scotland international after just 12 months, having seen him net 28 times in his debut campaign, and have sought to make it clear that the 23-year-old is not for sale.
Shaw told the Lancashire Telegraph on the Rhodes rumours: "We've had no contact from any club, and that's how we would like it to stay.
"There have been no bids for him. We do not want to sell him.
"When I flew out to India at the start of the summer, that was one of the things I wanted to clarify and I wanted to make sure that we could keep hold of our best players.
"Jordan is a very important player for us and he is a top professional. You only have to look at his goal return last season to see how much of an impact he has for us. We certainly have no desire to see him go."