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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.
Sunderland or Carlisle United v Kidderminster Harriers or Peterborough United
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