Ledley is available on a free transfer and the Championship club would get no compensation if Ledley moves abroad.
"If he moves to a club abroad we can't fight for compensation, "said Jones. "It would be the worst case scenario as Joe has been here since he was nine."
Players can leave clubs for no fee once their contract expires.
But if an English league footballer that has been at a club before the age of 23 moves to another domestic club, the old club can seek compensation from a Football Association tribunal for developing him.
If that home-grown player moves abroad before his 23rd birthday, the development club can seek minimal compensation - but if he moves abroad after his 23rd birthday, then the developing club cannot claim a penny.
Ledley celebrates his 23rd birthday on 23 January so clubs from Scotland, or any other foreign county for that matter, could sign him for no fee and no compensation in the summer.
If he doesn't stay here, let us hope Joe goes to a club in this county then we can fight our compensation
Cardiff City boss Dave Jones
The 32-times capped Welsh midfielder is supposedly being tracked by Premier League clubs such as Everton, Wolverhampton Wanderers and Stoke City.
Stoke boss Tony Pulis even had a £6m Ledley bid rejected for by Cardiff on the final day of the 2008 summer transfer window - and now the Bluebirds fear losing their prized asset for absolutely nothing.
And Ledley would be attracted to Celtic by the prospect of starring in the Champions League and playing regularly in front of 60,000 fans.
He could now sign a pre-contract agreement with a foreign club like Celtic as he is the final months of his current deal.
"We won't get anything if Joe moves abroad in the summer, it's as simple as that," Jones told BBC Sport.
"That would be a shame because we've spent a lot of time developing him and a lot of money has been invested in him.
"But I don't know why the compensation rule should apply in this country and not if he goes anywhere else.
"If he moves to a club in this country we will fight compensation - and rightly so.
"If he doesn't stay here, let us hope Joe goes to a club in this county then we can fight our compensation."
Ledley and his home-town club Cardiff, who have developed the player since the age of nine, have been in contract deadlock for four months and he has rejected two new deals.
Would Joe Ledley be a good signing for Celtic?
Ledley's representatives feel their client's wages should match his standing at the club and he is certainly one of manager Dave Jones' key players.
Another stumbling block between the two sides is Ledley's potential buy-out clause.
And Cardiff chief Ridsdale has already conceded that "unless things change, I expect him to be looking for pastures new in June."
Ledley, who helped inspire Cardiff to the 2008 FA Cup final at Wembley, captained his beloved club as the Welsh club narrowly missed out on a play-off place last season.
Jones stripped the academy graduate of the captaincy due to "speculation and uncertainly surrounding his future" in the summer.
But the manager hopes Ledley stays at Cardiff.
"If he stays here then it would be fantastic," Jones said. "It is up to us to persuade him to stay.
"At the moment, Joe hasn't mind his mind up."
Source: BBC Sport
Source: BBC Sport