The Cambridgeshire side are currently fourth in their league and beat Swindon Town 1-0 in the first round.
Histon will be winners in either scenario as the Cambridgeshire village lies only 52 miles from Northampton, making the fixture a local derby.
But the prospect of hosting Leeds at their 4,500-capacity Bridge Road ground has excited the Blue Square Premier's smallest club, especially if they are chosen for live television coverage.
The £75,000 fee Histon would receive represents a quarter of the club's annual £300,000 budget.
Chairman Gareth Baldwin said: "The publicity will be exceptional if it's Leeds because of the fact they are a monster of a club and we are a little village outfit. It will capture the imagination of the general public.
"They have enormous pedigree. It's not that long ago that they were in the Champions League semi-finals. Everybody at the club would be buzzing. If we get a TV game, it would be a big boost. We are pushing to get in the Football League and that could help us with one or two players to achieve that."
Curzon Ashton, who beat Exeter City 3-2, have a trip to Kidderminster Harriers while Blyth Spartans, who beat Shrewsbury Town, travel to Bournemouth.
The winning second-round clubs will receive £30,000 from the Football Association's prize fund.
Full FA Cup second round draw:
Chesterfield v Darlington/Droylsden AFC Hornchurch/Peterborough v Accrington/Tranmere Eastwood Town v AFC Wimbledon/Wycombe Wanderers Notts County v Kettering Town/Lincoln City Leicester City v Hereford United/Dagenham & Redbridge Eastbourne Borough/Barrow v Havant & Waterlooville/Brentford Bradford City v Leyton Orient AFC Telford United/Southend v Luton Town/Altrincham Team Bath/Forest Green Rovers v Barnet/Rochdale Histon v Leeds United/Northampton Town Scunthorpe United v Alfreton Town Torquay United v Oxford United/Dorchester Town Leiston/Fleetwood Town v Brighton/Hartlepool United Morecambe v Cheltenham Town Gillingham v Yeovil Town/Stockport County Millwall v Aldershot Town/Rotherham United Carlisle United/Grays Athletic v Crewe Alexandra Bournemouth v Blyth Spartans Kidderminster Harriers v Curzon Ashton Port Vale v Macclesfield Town
Ties to be played 29/30 November