Coventry, the winners of the competition in 1987, have suffered financial problems since their 34-year stay in England's top division came to an end in 2001.
Steven Pressley's side currently sit 10th in League One, having been hampered by a 10-point deduction for going into administration and play their home games at Sixfields in Northampton after being forced to leave their own home, the Ricoh Arena.
Chelsea will host fellow Premier League side Stoke City should they come through Sunday's third-round tie against Derby County, while Manchester City, who drew with Blackburn Rovers on Saturday, could face Bristol City or Watford in round four.
Former Hull City boss Phil Brown, now in charge of League Two Southend United, has been handed a reunion with his old club at Roots Hall.
Elsewhere, Manchester United or Swansea City face an away game at Birmingham City, Bristol Rovers or Crawley, with the latter two yet to play their second-round tie.
If Liverpool see off Oldham Athletic, they will head to Bournemouth or Burton Albion, while Everton are away to Stevenage, another lower-league side.
The draw in full:
Sunderland or Carlisle United v Kidderminster Harriers or Peterborough United
Bolton Wanderers v Cardiff City
Southampton v Yeovil Town
Huddersfield Town v Charlton Athletic or Oxford United
Port Vale or Plymouth Argyle v Brighton & Hove Albion
Nottingham Forest v Ipswich Town or Preston North End
Southend United v Hull City
Rochdale v Macclesfield Town or Sheffield Wednesday
Arsenal v Coventry City
Stevenage v Everton
Wigan Athletic or Milton Keynes Dons v Crystal Palace
Derby County or Chelsea v Stoke City
Blackburn Rovers or Manchester City v Bristol City or Watford
AFC Bournemouth or Burton Albion v Liverpool or Oldham Athletic
Birmingham City or Bristol Rovers or Crawley Town v Manchester United or Swansea City
Sheffield United v Norwich City or Fulham
