Monday's 3-0 loss at Crystal Palace leaves the Gunners in sixth place with seven games left to play, seven points off fourth-placed City having played one match fewer.
Arsenal are in serious risk of failing to qualify for next season's Champions League for the first time under Wenger, with the pressure on the manager reaching new heights in recent weeks.
Finishing below north London rivals Tottenham, also for the first time under Wenger, is an almost certainty but will be confident of beating a Boro side without a win in 14 top-flight games.
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Middlesbrough host Arsenal at the Riverside with kick-off scheduled for 8pm on Monday, April 17.
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Petr Cech (calf) and David Ospina (back) remain sidelined so the inexperienced Emiliano Martinez will continue in goal.
Cech is not expected to return before the Monday game but will be in contention to face Manchester City in the FA Cup semi-final.
Elsewhere, there is an outside chance Laurent Koscielny (Achilles) could return.
Middlesbrough could be boosted by the return of Gaston Ramirez from an ankle injury, but will likely only take a place on the bench.
The game will come too soon for Fabio and George Friend, while injured Calum Chambers would have been ineligible to face his parent club.
Middlesbrough starting XI: Valdes; Ayala; Bernardo, Gibson; Barragan, Clayton, Leadbitter, Forshaw, Downing; Stuani, Gestede
Arsenal starting XI: Martinez; Bellerin, Mustafi, Gabriel, Monreal; Xhaka, Elneny; Walcott, Ozil, Sanchez; Welbeck
BETTING ODDS (via 888 Sport)
- Middlesbrough to win: 11/2
- Arsenal to win: 13/25
- Draw: 33/10
Click here to place a bet. Odds correct as of April 12 at 2.45pm.