Javier Hernandez marked his first pre-season appearance with a goal as West Ham beat Angers 1-0 on Friday.
Everton are considering a £3m bid for West Ham defender Reece Oxford, Sky Sports News understands.
Crystal Palace have signed midfielder Cheikhou Kouyate from West Ham for an undisclosed fee on a four-year deal.
West Ham are in talks to sign four players from the Portuguese Primeira Liga, including internationals Moussa Marega and Yacine Brahimi.
Crystal Palace are closing in on the signings of Max Meyer and Cheikhou Kouyate, Sky Sports News understands.
There were pre-season wins for West Ham United, Crystal Palace and Huddersfield Town on Tuesday night.
West Ham want to give Domingos Quina a new contract after he helped Portugal win the U19 European Championship, Sky Sports News understands.
Marko Arnautovic has praised the impact of West Ham's new signings following the club's 2-1 win over Ipswich at Portman Road on Saturday.
Wilfried Zaha starred for Crystal Palace in a thumping pre-season win over Reading, while Mason Mount scored the winner for Derby against Wolves.
Fulham, Burnley and West Ham were all in talks to sign Alfie Mawson from Swansea on Friday, according to Sky sources.