The Blues reportedly made contact with Pastore's representatives last season but couldn't hammer out a deal for 27-year-old Argentina international.
Pastore ended up remaining in the French capital but, with Antonio Conte keen to strengthen his squad with Champions League football next season, Chelsea are set to rekindle their interest, according to reports in Italy.
PSG themselves have been linked with a potential move for Costa, which could add some spice to negotiations.
The French champions are big fans of the Chelsea striker, whose goals are helping to power the Blues towards this season's Premier League title.
And so the prospect of a swap deal could well jump onto the agenda, if both sides are willing to do business.
Pastore has won four Ligue 1 titles, three French League Cups and two French Cups during his time at PSG.