"We have had a seven-figure offer for Aaron, but we had absolutely no hesitation in turning it down," Ridsdale told the Western Mail.
"The trouble with offers like these for such a young player is that while the headline numbers are impressive, they tend to be structured in such a way that you don't get the full amount until five years' time.
"That said, the fact that a leading club has come in with such a big bid for Aaron says everything about him, really.
"He is a young player with huge promise, but our aim is to see that promise and potential fulfilled at Cardiff City.
"We have an academy system in place here which is designed to get the best young players around to play for us, not to sell them.
"At some time, we appreciate a knockout blow may be delivered in terms of a bid we believe we cannot turn down for Aaron.
"But even though this is a seven-figure offer, we still don't believe it is high enough at this moment in time for a player like Aaron."
Ridsdale would not name the club who made the bid but it follows bids for Chris Gunter from Everton. When asked about turning down over £2m worth of bids for the two players Ridsdale said
"I'm desperately trying to put a squad together to demonstrate our ambition at this club.
"Ideally, we would like to see Aaron and Chris Gunter play for many years in a Cardiff City shirt."
Ramsey is the Wales U17 captain and a key player for City's academy side.
It's also been reported that Birmingham City are interested in a more experienced youngster. Joe Ledley, himself only 20, is said to be attracting interest from the Midlands club.