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Goalkeeper and captain Lloris has a thigh injury while midfielders Alli and Sissoko have hamstring problems that saw them miss Saturday's 2-1 Premier League home loss to Liverpool.
The 22-year-old Tottenham Hotspur star suffered the injury in Saturday's 2-1 defeat to Spain in the Nations League.
Mauricio Pochettino's side are the first club in the Premier League era not to make a single signing since the introduction of the pre-season transfer window.
Alli caught the eye of Spurs' scouts playing in English football's third tier for MK Dons in Milton Keynes and remembers all too well the harsh lessons he learned on the way.
For Sweden, who failed to qualify for the previous two World Cups, it was their best result since finishing third at the 1994 finals.
People erupted in celebration and the beer went flying as England reached the World Cup semi-finals for the first time in 28 years.
Goals from Harry Maguire and Dele Alli and a string of fine second-half saves from goalkeeper Jordan Pickford were enough for England to progress to the last four.
England comfortably beat Sweden 2-0 on Saturday to reach the World Cup semi-finals for the first time in 28 years.
England have lost six times out of seven on spot-kicks at major tournaments, with their coach Gareth Southgate guilty of missing against Germany at Euro 96.
Alli possesses a goal threat that Loftus-Cheek lacks and, crucially, England need if they are to take the burden away from their free-scoring captain.
Dele Alli picked up the knock during the 2-1 win over Tunisia with him tweeting that he was working to get back to full fitness.
The 22-year-old has six days to recover before Sunday's game against Panama, with Marcus Rashford and Loftus-Cheek both potential replacements.
Alli, who has come under scrutiny for previous incidents of hot-headed behaviour at Tottenham Hotspur, remains confident he will avoid letting his temper get the better of him in Russia.
Some pundits fear Alli could suffer the same fate as David Beckham, who was infamously sent off in the 1998 World Cup after being provoked by Argentina's Diego Simeone.
Dele Alli scored twice as Tottenham beat Chelsea 3-1 to end a 28-year wait for an EPL win at Stamford Bridge.