Nottingham Forest are the club after Peter Whittingham. Their offered of £1m will need to be upped to take the former Aston Villa player back to the Midlands.
Forest have already signed former City striker Robert Earnshaw for £2.65m.
"We firmly believe Roger and Glenn Loovens are probably the best central defensive partnership in the Championship," said Peter Ridsdale.
"Therefore our objective this summer is to keep those two players together to ensure our best push at the league next season.
"The only way we'd consider selling Roger, or Glenn for that matter, is that if we received a knock-out bid and the manager thinks we could replace them.
"The bids for Peter and Roger just shows how shrewd we've been in the transfer market," added Ridsdale.
"As we bought both players for just a quarter-of-a-million and now we're rejecting bids of more than £1m for the both of them." Ridsdale did reveal the futures of superstar strikers Robbie Fowler and Jimmy Floyd Hasselbaink will depend on how successful manager Dave Jones is in his search for striking reinforcements.
Both one-time Premier League goal kings signed one-year deals at Ninian Park last summer with an option for another season.
Hasselbaink endured a stuttering season in South Wales while Fowler hasn't played since mid-December due to a hip injury.
Ridsdale said: "Dave has given me his transfer targets and clearly we need strikers next season to give us a better shot at promotion.
"Robbie and Jimmy's futures at Cardiff will depend totally on if we are able to bring strikers to the club."