Wenger is under intense pressure following a humiliating 5-1 loss away to German giants Bayern Munich.
The tie of the fifth round, at least for those who still believe in the "romance of the Cup", sees non-league Sutton at home to joint-record 12-times Arsenal on Monday.
Arsenal will make the trip from north to southwest London, for a match on the artificial pitch at Sutton's Gander Green Lane ground, with Wenger under intense pressure following a humiliating 5-1 loss away to German giants Bayern Munich in the first leg of a last 16 Champions League tie.
That defeat came hot on the heels of a recent shock league loss to Watford and an ensuing, rather more predictable defeat by Chelsea that between them appeared to have scuppered he Gunners' hopes of a first Premier League title since 2004.
Even those once loyal to veteran manager Wenger, in charge at Arsenal since 1996, have started to question whether the 67-year-old Frenchman will seek a renewal of his contract when it expires at the end of the season.
But Sutton boss Paul Doswell, whose side beat second-tier Leeds in the fourth round, was blunt when asked about Wenger's plight.
"Do I feel sympathy for him? No. He is well schooled, and he has been in the job for 20 years," said Doswell, whose team are currently 17th in the National League, the fifth tier of English football.
Wenger accepted Arsenal had "collapsed mentally" against Bayern and Gunners defender Laurent Koscielny, who went off injured four minutes into the second half with the score at 1-1, could not explain why.
"I don't know either," he told Arsenal TV. "I think the first half was good -- we were deep, like you need to be, and tried not to give them space or opportunities to score."
Lincoln City, the other non-league side to make it to the fifth round, will also face Premier League opposition when they travel to Burnley on Saturday.
"We approach it the same way we do any team," said Burnley manager Sean Dyche. "There's not a divine right to win football matches."
Premier League leaders Chelsea travel to second-tier Wolves, with Pedro praising the impact made by Blues manager Antonio Conte since his pre-season arrival.
"With this coach, all the team is focused on the fight for the title, with more confidence for every game and this is good," said the Spanish winger. "It's a completely different season."
Manchester City, away to Championship high-flyers Huddersfield, will be without Gabriel Jesus after the striker, who had scored three goals in as many league games since his January arrival, broke a metatarsal bone in a league win at Bournemouth.
Pep Guardiola’s decision over a replacement is complicated by the looming Champions League last 16 first leg tie at home to French club Monaco, on Tuesday.
The City manager faces a choice between fans' favourite Sergio Aguero, who lost his starting place to Jesus, or Nigeria's Kelechi Iheanacho.
"I know how important Sergio is," said Guardiola after the Bournemouth win. "I did yesterday, the day before, the last week, the last month."
Saturday will also see third-tier Millwall try to inflict more misery on faltering Premier League champions Leicester, now just a point above the relegation zone, with top-flight Middlesbrough up against another League One side in Oxford.
Holders Manchester United, like Arsenal 12-times Cup winners, are away to Championship strugglers Blackburn on Sunday fresh from Zlatan Ibrahimovic's hat-trick in a 3-0 win over St Etienne in the first leg of their last 32 Europa League tie on Thursday.
Meanwhile Tottenham Hotspur, beaten 1-0 by Gent in the Europa League, will also face Championship opposition when they travel across London to Fulham.
FA Cup 5th rd
Fixtures (1500 GMT unless stated)
Saturday: Burnley v Lincoln (1230 GMT), Huddersfield v Manchester City, Middlesbrough v Oxford, Millwall v Leicester, Wolves v Chelsea (1730 GMT)
Sunday: Blackburn v Manchester United (1615 GMT), Fulham v Tottenham (1400)
Monday: Sutton v Arsenal (1955 GMT)