The Hammers are in the market for attacking reinforcements after selling Marko Arnautovic and Lucas Perez over recent weeks, while they released Andy Carroll at the end of last season.
Jordan Hugill and Javier Hernandez are currently the only senior strikers within Pellegrini's squad and speculation continues to link the latter with a move away from the club.
West Ham remain hopeful of signing Maxi Gomez from Celta Vigo, although those talks have stalled after the two clubs failed to agree on a payment structure for the player's £45 million release clause.