The Argentina star has caught the eye of the managerless Blues as they look to add a creative force to their midfield, with Tottenham's Luka Modric another reported target.
Palermo are aware of Chelsea's interest in 21-year-old attacking midfielder Pastore, but claim Primera Liga giants Barca and Real are also gunning for his signature.
"Chelsea, Real Madrid and Barcelona want Pastore," Palermo president Maurizio Zamparini was quoted as saying in The Sun.
"I told his agent to see what market there is for the player and he has probably spoken to some clubs.
"At the end of the week we will meet to shed a bit of light on the future of the player."
Zamparini has slapped a 50million euros (?44million) price tag on Pastore, who is contracted at Palermo until 2014, and is thought to be unwilling to sell him to a rival Serie A club.
Source: Team Talk
Source: Team Talk