The FA Cup holders have been heavily linked with a move for Blackburn's star man after manager Owen Coyle refused to confirm or deny whether the club had made an official enquiry about the striker.
Despite continuingly insisting Rhodes is not for sale, Blackburn know a bid for last season's top scorer from the Premier League could bring about a challenge to keep their man.
However, Shaw has stated that this is not the case if a fellow Championship club come calling.
He told the Lancashire Evening Telegraph: "We have no plans to sell Jordan and we don't want to sell him. He's not for sale.
"If it was a Premier League club it might be a different case because Jordan would probably want to go.
"But we have no plans to sell to another club in the Championship and he is not for sale, as we've said all summer.
"We're trying to get out of this division so we certainly wouldn't want to sell to a competitor in the Championship."
Bolton were also linked with a move for the former Huddersfield man, however, Dougie Freedman was quick to rule out any swoop.
Blackburn are still looking to strengthen their own squad this summer but with West Bromwich Albion reportedly still looking at the 23-year-old, Shaw admits the transfer window creates unwanted frustration when trying to keep hold of star players.
"I know a lot of managers have had things to say about the transfer window and I agree with them, it's not for me," he said.
"You're still unsure about players and we've had a month of the season gone now.
"You get an enquiry that ends up in the papers but that's not my way of doing things or Blackburn Rovers' way of doing things.
"We are working hard on certain things but until it's done we'll keep things to ourselves.
"We're trying hard to get one or two things done and we'll see what happens."