The campaign resumes provisionally on June 17, with the Hammers expected to host Wolverhampton Wanderers a few days later.
They have already played a friendly that lasted around 60 minutes between their first-team squad in full kit at the London Stadium last Saturday, but Moyes wants to raise the bar and is hoping to have his side play against the Gunners and Eagles to get his team match-fit.
The Premier League have approved friendly games, but teams must not travel further than 90 minutes, and players must get to the stadiums alone in their cars without the normal team bus.
West Ham want to play Arsenal and Palace having already faced them twice in the Premier League this term, and it remains to be seen where the games will be staged as the friendlies can be played at either the clubs’ stadiums or training grounds.
The Hammers are currently 16th in the top-flight table with nine games left, and only a superior goal difference separates them from 18th-placed Bournemouth, while two points stand between them and 19th-placed Aston Villa – who have a game in hand.
West Ham host Wolves, Chelsea, Burnley, Watford and Villa at the London Stadium, and have trips to Tottenham Hotspur, Newcastle United, Norwich City and Manchester United in their remaining fixtures.