The Argentinian playmaker would be required to take a significant pay cut should he choose to join the London club, the Guardian claim.
Pastore, who joined PSG from Palermo for £37m in 2011, reportedly earns £160,000-a-week in Paris, and even with the Premier League's television money new Hammers boss Manuel Pellegrini isn't in a position to offer the creative player that kind of wage.
The once highly-rated player has found himself rapidly falling down the pecking order at PSG, starting just 16 games in all competitions last season, and may seek an exit to help reignite his career. Pellegrini, meanwhile, was reportedly close to signing the 28-year-old during his final season at Manchester City in 2015.
It is understood that the West Ham board are willing to back their newly appointed Chilean manager with some major signings, and Pastore would fit the bill should he accept the wage cut.
West Ham in talks to sign PSG midfielder Javier Pastore. PSG willing to sell this summer.€20m deal— Kaveh Solhekol (@SkyKaveh) June 1, 2018
The Argentine would help ease the pressure on compatriot and current Hammers creative outlet Manuel Lanzini. Pastore has scored 45 goals and provided 59 assists across 265 appearances for the Parisians.
PSG are in desperate need of offloading players this summer too, given their ongoing issues with Financial Fair Play regulations.
While the player would need to agree a huge reduction in wages for any deal to go through, the player could be encouraged to having seen his career begin to falter in the French capital. His lack of game time this season cost him a place in Argentina's World Cup squad.
West Ham are also targeting moves for William Carvalho and Ryan Fredericks, as Pellegrini carries out a major overhaul of the current playing squad.
A number of current first team squad members have also been told they do have a future at the London Stadium and are free to leave.