Italians will need to get through two one-leg matchups to advance in a newly devised playoff system. The draw takes place on Nov. 26 and Italy will be at home for its first match.
The 28-year-old Kane could well be rested after lighting up Wembley Stadium by taking his England tally to 44 goals, nine from catching Wayne Rooney's national record.
Mount will be in the Chelsea squad for Saturday's Premier League clash at home to Burnley, but is unlikely to start and may be forced to have dental treatment on the problem.
Wins for Scotland, Serbia, Sweden, Switzerland and Ukraine moved each closer to at least a place in the playoffs next year with the finals tournament in Qatar in sight.
The 21-year-old Sancho moved to United from Borussia Dortmund in the offseason for $100 million.
Raheem Sterling, Harry Kane and Harry Maguire scored in a 14-minute flurry and Declan Rice added a fourth second-half goal.
'Bring it home': Queen Elizabeth II, Prince William wish England football team success ahead of Euro final
Prince William, the President of England's Football Association (FA), on Sunday released a video message wishing the squad led by captain Harry Kane the "very best of luck for tonight".
Maguire was a major doubt for the European Championship, but Gareth Southgate waited on him even though the former Leicester defender was not fit until the third group game.
It marked the first time that England scored four goals in the knockout stage of a major tournament since beating West Germany 4-2 in the 1966 World Cup final.
AS Roma coach Jose Mourinho has said England should be able to reach the finals of the ongoing Euro 2020.
England managed to progress to the round of 16 stage after finishing the Group D toppers following a win over Croatia and the Czech Republic.
Southgate has restored the reputation of the England national team from the lows of a humiliating Euro 2016 exit against Iceland in the round of 16 and the ignominy of Sam Allardyce's brief tenure.
At the European Championship, it's meant the playing availability of Mount and Chilwell is more in the hands of the Public Health England government agency than national team coach Gareth Southgate.
The Scottish sides of 1967 and 1977 are still fondly remembered for victories at Wembley in the old British Home Championship.
Gareth Southgate's lack of a stellar coaching CV at club level has counted against him in the eyes of his doubters.