Randolph is set to start in goal as Adrian begins a three-match suspension following his sending-off against Leicester last weekend.
Mauro Zarate (hamstring) has joined his fellow strikers Enner Valencia (leg) and Andy Carroll (knee) in the Hammers’ treatment room, while midfielder Reece Oxford is a doubt after missing a few days’ training this week with a niggle.
Bournemouth manager Eddie Howe, meanwhile, is expected to keep faith with the team which has lost its opening two Premier League fixtures.
Harry Arter (groin) Christian Atsu (back) remain on the sidelines for the Cherries.
This will be the first league meeting between West Ham and Bournemouth since April 1990 and only their third overall in league competition.
Bournemouth have not won any of their previous five competitive meetings with the Hammers (D2 L3).
Bournemouth have lost their opening two games – only one of the six newly-promoted sides to lose their opening three games of a PL season has gone on to avoid relegation (Southampton in 2012-13).
Goalkeeper Adrian will miss this match for West Ham following his red card against Leicester – the Spaniard had started each of the last 58 PL matches for the Hammers.
West Ham back-up keeper Darren Randolph has conceded 16 goals in his last three appearances against Bournemouth, including 12 in two games last term.
The Cherries have given Premier League appearances to 10 different English players in their opening two games of 2015-16; more than any other side.
Andrew Surman has made the most passes in both of his Premier League appearances so far this season and has made the most overall in the PL after two weeks (167).
Callum Wilson has had 19 touches in the opposition box so far this season; only Alexis Sanchez (20) has had more.
Since the start of 2014-15, Callum Wilson has won more penalties alone (11) than 92 of the 93 other clubs (excluding Bournemouth themselves) to have played in the top four tiers since then (the exception being Swindon – 14).
Mark Noble has been fouled 10 times in the opening two match days of the 2015-16 season, more than any other player.
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