The Blues were this morning handed a trip to Haig Avenue – and a reunion with their former manager – in the draw for the fourth qualifying round of the competition.
The tie will be played on Saturday, October 15.
Burr was in charge of Chester for just over two years but was sacked in April following a run of poor results. His number two, Jon McCarthy, impressed enough during a spell as caretaker to be appointed his full-time successor, and the former Northern Ireland winger has guided the Blues on a five-match unbeaten run which has lifted them to 12th in the table.
Burr replaced Andy Bishop at National League strugglers Southport in early September and has picked up five points from a possible 15.
The Blues' FA Cup journey ended at the first hurdle last season, as they lost 1-0 at Altrincham in the fourth qualifying round.
However, the season before they made it to the second round proper, losing out to Barnsley in a replay after a memorable first-round success at Southend United.
Chester were ball number two in the northern section of today's draw. If they overcome Southport, they will reach the first round proper and also bag £12,500 in prize money.
Here's the fourth qualifying round draw in full:
Southport v Chester FC
Alfreton Town v Gateshead
North Ferriby United v Macclesfield Town
FC United of Manchester/Harrogate Town v FC Halifax Town
Stockport County v Bishop Auckland
Barrow AFC v Tranmere Rovers
Halesowen Town/Nantwich Town v Stourbridge
Altrincham v Matlock Town/Workington AFC
Lincoln City v Guiesley AFC
Lincoln United v Spennymoor Town
Stamford AFC v Wrexham
York City v Curzon Ashton
Welling United v Whitehawk
Westfields v Leiston
Sutton United v Forest Green Rovers
Chesham United v Potters Bar Town/Bath City
Dagenham & Redbridge v Wealdstone
Torquay United v Woking
Taunton Town v Gloucester City/Hemel Hempstead Town
Braintree Town v Bromley
Beaconsfield SYCOB v Brackley Town
Tonbridge Angels v Dartford
Faversham Town/Egham Town v St Albans City
Boreham Wood v Hendon
Aldershot Town v Eastbourne Borough/Hadley
Harrow Borough v Margate/Hastings United
Maidstone United v Billericay Town
Kidderminster Harriers v Weymouth
Solihull Moors v Kettering Town
Burgess Hill Town v Dover Athletic
Merstham v Ebbsfleet United
Eastleigh v North Leigh