The Dolly Blues are scheduled to travel to NPL East Division high flyers Liversedge in the second round proper.
A pitch inspection took place at lunch time and the Yorkshiremen have declared that as it stands the game will take place this evening.
The tie was originally scheduled to take place on Saturday, but the weather forced the game to be postponed.
There is a possibility that this evening's game could go the same way.
If City eventually progress beyond this round then they will face Morpeth Town in the next round.
The North East outfit edged past Warrington Town on penalties at the weekend.
It will be the third time that City will travel to Morpeth this season having played at Craik Park twice already, once in the league and once in the FA Cup.
The league encounter ended all square at 2-2 but the cup clash was a 4-1 defeat.
City boss Mark Fell is not looking beyond this evening's fixture.
Although in the division below City, it could be argued Liversedge are marginally the favourites.
They are unbeaten in the league and are formidable at home having won all six of their home games.
"It's a big game," said Fell. "We will be going there to win the game and we back ourselves.
"Make no mistake it's going to be a tough game.
"They are well resourced after a new chairman took over three years ago.
"You just need to look at some of their players - they have got National League-standard players.
"So we are under no illusions how difficult it is going to be."
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