The annual fixture traditionally takes place between the Premier League champions and the holders of the FA Cup.
But the FA could invite the winners of the Championship to compete in their place, according to The Times.
Leeds currently sit second in the Championship, two points behind leaders West Brom, but with a game in hand.
The two sides last met in the Charity Shield back in 1992, when Leeds were last champions of England.
Howard Wilkinson’s side were victorious over Graeme Souness’ men that day, with Eric Cantona scoring a hat-trick in a 4-3 thriller.
The hint of a rematch has been raised due to the late finish of this season’s Champions League and Europa League, which is causing havoc with the fixture schedule.
Manchester United, Chelsea and Manchester City are all in the semi-finals of the FA Cup and remain in the hunt for silverware in Europe’s major competitions.
The FA have pencilled in August 23 as a possible date for the game, but that would clash with the rescheduled Champions League final in Lisbon.
Instead of cancelling the event, they are exploring options for the opponents of Premier League champions Liverpool.
The FA are also believed to be looking into the feasibility of the game as a test event for the return of fans after the coronavirus lockdown.
There is precedent for different teams to be invited by the FA to take part.
In 1971, champions of the old Second Division, Leicester, played FA Cup runners-up Liverpool when double winners Arsenal declined to take party due to previously-arranged friendly commitments.