Dimitri Payet left West Ham in controversial circumstances (Image: Getty)
According to the Guardian, Payet's representatives have offered the 31-year-old to the Hammers.
The Marseille ace will likely be available for around £25m but may split fan opinion upon his return to the club.
Payet handed in a transfer request while West Ham were battling relegation, which led to a falling out between the player and the board.
Ian Wright on Dimitri Payet: They should get rid of him
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Co-owner David Sullivan accused the midfielder of betrayal, while Payet fired back, saying he was 'bored' of playing for a struggling team.
West Ham are expected to confirm the signing of Jack Wilshere on a free transfer in the coming days.
Pellegrini has already added the likes of Lukas Fabianski, Ryan Fredericks and Issa Diop since taking over in May.