West Ham are hopeful of signing free agent Brazilian midfielder Bernard.
The 25-year-old left Shakhtar Dontesk at the end of the season and the London Stadium club believe they can bring him in before the summer window slams shut.
West Ham have also discussed a possible loan return for Inter Milan's Joao Mario, who impressed under David Moyes last campaign.
They also have an interest in Juventus' 25-year-old midfielder Stefano Sturaro.
Everton have expressed an interest in signing West Ham defender Reece Oxford.
Manuel Pellegrini kicks off his reign at West Ham with a game against Liverpool in the Premier League on August 12.
They continued their preparations for the new campaign with a 1-0 victory against Angers on Friday night. Javier Hernandez scored the only goal of the game.