Rovers captain Scott Dann, who scored the equaliser in the 1-1 FA Cup draw with Manchester City, is believed to be on Crystal Palace's wanted list, with the Eagles considering lodging a bid of around £2.5million.
Bowyer is aware he needs to trim the club's wage bill after signing Tom Cairney and Rudy Gestede for a combined £800,000.
But the Rovers manager insists he is under no pressure to sell, and will only consider offers for players if they match his valuation.
He told the Lancashire Telegraph: "If people are interested in our players and make sensible bids then we will consider them.
"We do have to reduce in certain areas and certain players that's for sure.
"But we are not a charity case."
One player who will not be leaving Ewood Park in January is top-scorer Rhodes, who scored 30 league goals in 2013 - more than any other player in English professional football.
The Scotland striker has been linked with an £8m move to Championship rivals Nottingham Forest.
But Bowyer insists the prolific marksman is staying put, saying: "Jordan Rhodes isn't for sale.
"I was never very good at maths but we paid £8m for him, then he goes and scores the most goals in the calendar year - more than Luis Suarez - and yet he is still valued at £8m.
"That doesn't quite add up to me - but then again I'm no Carol Vorderman!"