The Blues baulked at the Italian club's incredible ?44million asking price earlier this summer but have maintained an interest in the midfielder, who is also believed to be on the radar of Spanish trio Barcelona, Real Madrid and Malaga.
But the Serie A outfit's president Maurizio Zamparini has warned clubs interested in signing the 22-year-old must make their move in the next 15 days.
Make a move: Palermo are inviting bids for Javier Pastore, the Argentina playmaker who is on Copa America duty in Buenos Aires
Palermo confirmed last month they had received a 50m euros bid from an unnamed club to acquire Pastore, who is under contract until 2015 and currently on international duty at the Copa America.
And Zamparini said: 'The only Palermo player that is in the market is Pastore.
'The situation must be resolved in the next 15 days, otherwise, the player will remain with us.
'Before the Copa America ends, Pastore's future must be decided.
'There is a 90 per cent chance that Pastore will leave because that is his desire and when you hear about the clubs that want him it's only normal.
'We would be sad to see him go, considering he is the only star that I've had as president.'
The highly-rated playmaker joined Palermo in 2009 from Huracan for 19million euros and was the team's leading scorer in Serie A last season with 11 goals.
Meanwhile, Pastore's international colleague Ezequiel Lavezzi has yet to receive a good enough offer to leave Napoli this summer, according to the player's agent.
Staying power: Argentina's Ezequiel Lavezzi will not leave Napoli unless he receives the right offer
The striker has been strongly linked with a move to the Barclays Premier League, with Manchester City and Liverpool among the clubs reportedly keen to acquire the his signature.
'Lavezzi will not move unless an important offer arrives,' Lavezzi's agent Alejandro Mazzoni told Italian newspaper Gazzetta dello Sport.
'At this time, there are none.'
The 26-year-old forward, who is also a reported target of Barcelona, is under contract with Napoli until June 2015 but has a release clause in his contract of 30m euros.
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