The Daily Record says the Championship club, who had already offered the 23-year-old a contract worth Â£20,000 a week - are now prepared to go even further in a last-ditch move to hold on to their Â£5million- rated midfielder.
The surprise twist came less than 24 hours after Ledley had been given a VIP tour of Celtic's Lennoxtown HQ and during his whistle-stop visit, opened talks on a possible Bosman transfer.
Ledley, who has been identified by manager-in-waiting Neil Lennon as a priority summer target, will now head off on holiday to Portugal today and take time to weigh up all of his options.
It was wrongly claimed yesterday the player was in Italy to discuss a possible switch to Roma when, in fact, he was listening to what Cardiff had to offer.
Ledley is also interesting Greek outfit Panathinaikos, Turkish big guns Fenerbahce and Galatasaray as well as a string of mid-table clubs from England's Premiership, including Stoke, Fulham, Blackburn and Wigan.