The Exiles have reached this stage of the competition for the first time since 1949, having seen off Metropolitan Police, Wrexham, Leicester and Middlesbrough so far.
However, they can be backed at a massive 28/1 (29.00) with bet365 to pull off another massive upset by defeating the reigning Premier League champions, and 12/1 (13.00) to take the game into extra-time with a draw.
Pep Guardiola's men have scored 12 goals without reply in their two FA Cup ties so far, and are 1/20 (1.05) favourites to ease to victory here.
Claudio Bravo, Benjamin Mendy and Vincent Kompany are the only injury doubts for Guardiola, although he may choose to field a heavily rotated team ahead of the Champions League game against Schalke and Carabao Cup final versus Chelsea.
Mark O’Brien and Joss Labadie should be fit to play after sitting out Tuesday's defeat against MK Dons, although new signing Ade Azeez is cup tied.
While they have dished out some heavy beatings in both domestic cup competitions this season, the Citizens will have bad memories of exiting last season's FA Cup at this stage with a shock 1-0 defeat at Wigan.
Although another upset seems unlikely, Rodney Parade's famously poor playing surface shared by two rugby teams should at least prevent the guests from hitting top gear.
Indeed, Mike Flynn's team have let in just two goals in their last seven home matches, and conceded only three times in four FA Cup home games against higher level opponents Leeds, Tottenham, Leicester and Middlesbrough over the last two campaigns.
With City bound to be keeping one eye on the important fixtures ahead of them, odds of 4/5 (1.80) could prove a wise investment on them being restricted to under 4.5 goals in a narrow win over determined Newport.