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Alex song returns to the starting line-up against his former club after he was rotated out of the starting line-up last match.
The one time ‘Invincible’ came on as a substitute against Chelsea on Boxing Day.
Jenkinson is unavailable for the Hammers as he is on loan at the club from their London rivals.
Diafra Sakho also starts alongside Andy Carroll as part of a striker rotation that looks to keep fresh over the festive period.
Meanwhile, there are three changes for the Gunners as Laurent Koscielny, Francis Coquelin and Alex Oxlade-Chamberlain come in for Kieran Gibbs, Tomas Rosicky and Olivier Giroud.
Giroud begins his three game suspension following a sending off for a headbutt on Nedum Onuoha in Arsenal’s boxing day clash with QPR.
Laurent Koscielny returns for Arsenal as he recovered from a calf injury that has kept him side-lined since the start of December.
West Ham starting XI: Adrian, O'Brien, Tomkins, Reid, Cresswell, Song, Amalfitano, Kouyate, Downing, Sakho, Carroll.
Substitutes: Nolan, Noble, Collins, Demel, Jaaskelainen, Cole, Valencia.
Arsenal starting XI: Szczesny, Debuchy, Mertesacker, Koscielny, Monreal, Oxlade-Chamberlain, Flamini, Coquelin, Sanchez, Welbeck, Cazorla.
Substitutes: Gibbs, Podolski, Ospina, Walcott, Chambers, Campbell, Akpom.
Speaking after their 3-2 victory over QPR, Wenger admitted that Giroud had made a 'big mistake' following his apparent headbutt on Nedum Onouha.
"Yes, of course," said Wenger when asked if he would have stern words with Giroud behind the scenes.
"He knows that he has made a big mistake today. It was deserved, he didn't control himself and that of course, is a straight red.
"Of course (it was costly), it changed the game's dynamic completely.
"We were completely in control of the game, not in trouble, and suddenly we were down to 10 men and only one-nil up.
"We threw our bodies in after that.
"We knew we had to do that, and what I feel is that in the last four, five weeks we have defended with more resilience, even if we conceded from a set-piece to draw against Liverpool.
