Everton will host Salford City in the second round of the Carabao Cup, with an away tie against Fleetwood Town or Port Vale awaiting them in the third round.
The Toffees’ route to Wembley will begin in the week commencing September 14, when they welcome Salford, 11th in League Two last season, to Goodison Park.
And if they get past Salford, Everton will travel to the winner of the second-round tie between Fleetwood and Vale in the third round.
The third round ties are scheduled for the week commencing September 21, with the fourth round pencilled in for the week commencing September 28.
All of these above EFL Cup clashes will, of course, be played behind closed doors as a consequence of the coronavirus pandemic.
It will mean Everton could face as many as six games in the first two-and-a-half weeks of the new season, ahead of the proposed re-opening of fans to stadia on October 1.
Everton have never previously played Salford, who are perhaps best-known for being part-owned by former Manchester United players Phil and Gary Neville, Nicky Butt, Paul Scholes, Ryan Giggs and David Beckham.
Fleetwood, managed by Joey Barton, finished sixth in a truncated League One last season but failed in the play-offs, with John Askey’s Port Vale ending up eighth in the curtailed League Two table last term.
Everton - potential September fixture list
Sunday, September 13 - Tottenham vs Everton (Premier League, 4.30pm BST)
Week commencing September 14 - Everton vs Salford City (EFL Cup second round)
Saturday, September 19 - Everton vs West Brom (Premier League, 12.30pm BST)
Week commencing September 21 - Fleetwood or Port Vale vs Everton or Salford City (EFL Cup third round)
Saturday, September 26 - Crystal Palace vs Everton (Premier League, 3pm BST)
Week commencing September 28 - EFL Cup fourth round
The full Third Round draw for the Carabao Cup is below -
Bradford City / Lincoln City v Liverpool
Bristol City / Northampton Town v Burton Albion / Aston Villa
Morecambe / Oldham Athletic v Newcastle United / Blackburn Rovers
Reading / Luton Town v Manchester United
Derby County / Preston North End v Brighton & Hove Albion / Portsmouth
Ipswich Town / Fulham v Rochdale / Sheffield Wednesday
Manchester City v AFC Bournemouth / Crystal Palace
West Ham United / Charlton Athletic v Leeds United / Hull City
Millwall / Cheltenham Town v Burnley / Sheffield United
Chelsea v Middlesbrough / Barnsley
Wolverhampton Wanderers / Stoke City v Gillingham / Coventry City
Leicester City v Arsenal
West Bromwich Albion / Harrogate Town v Southampton / Brentford
Newport County / Cambridge United v Oxford United / Watford
Fleetwood Town / Port Vale v Everton / Salford City
Leyton Orient / Plymouth Argyle v Tottenham Hotspur