Alloa will have to negotiate non-league opposition away from home if they are to reach the fourth round of the Scottish Gas Men's Scottish Cup.
The Wasps, and their fellow clubs in League One, are entering the competition at the third round stage, the draw for which took place on Sunday evening.
Conducting the draw was Scott Bain, the current Falkirk and Scotland squad goalkeeper, who spent three years at the Recs.
After leaving Aberdeen, he signed for the club in 2011 and, in a three-year spell, helped them to back-to-back promotions from Division Three (now League Two) to the Championship, before moving on to Dundee.
Bain, a three-time winner of the trophy with Celtic, whom he left Dundee for in 2018, prior to joining the Bairns last summer, picked his old club out to travel to either Threave Rovers or Pollok.
Based in Castle Douglas, Dumfries and Galloway, Threave are fifth in the West of Scotland League, First Division, whilst Pollok, who play on Glasgow's southside, are two tiers higher, sitting second in the Lowland League West.
They had been due to meet in the second round on Saturday but, due to the impact of Storm Boelo, the game was called off.
It has now been rescheduled for this Saturday, the winners of which will take on the Wasps, over the weekend of Saturday November 28.
Andy Graham's side will hope to reach round four for the first time since 2023/24, when they lost at Premiership Motherwell, having been knocked out by Dumbarton, and Raith Rovers, at the first hurdle in each of the last two seasons respectively.
The third round draw in full is:
Troon v Raith Rovers
Montrose v Hamilton Academical
Queen of the South v Dunfermline Athletic
East Kilbride v Penicuik Athletic or Clyde
Bo'ness United v Brechin City
Annan Athletic v Greenock Morton
Cumnock Juniors v Arbroath
Elgin City v Partick Thistle
Dumbarton v Johnstone Burgh or Formartine United
Stranraer v Clachnacuddin
Peterhead v Edinburgh City
Threave Rovers or Pollok v Alloa Athletic
Queen's Park v The Spartans
Ross County v Brora Rangers
Hill of Beath Hawthorn or Musselburgh Athletic v Airdrieonians
Clydebank v Livingston
Renfrew v Cumbernauld Colts or Banks O'Dee
Inverness Caledonian Thistle v Cove Rangers
Stenhousemuir v East Fife
Largs Thistle v Ayr United.
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