The 28-year-old contributed four goals and five assists from 25 appearances in Ligue 1 this season, but 11 of those outings came from the substitutes' bench.
Pastore, who has one year left on his PSG contract, is thought to be available for transfer as the Parisians aim to comply with UEFA's Financial Fair Play regulations.
According to Sky Sports News, the Argentina international is currently asking for wages of up to £190,000-a-week, which the Hammers are hoping to drive down.
The report adds that West Ham are eager to bring Pastore to the club and remain in talks over a deal that would be worth up to £17.5m.
Pastore, who joined PSG from Italian side Palermo in 2011, has scored 45 goals in 265 appearances for the French champions.