Manchester City's De Bruyne (ankle) and Real Madrid's Hazard (muscle strain) were both forced out of Belgium's 1-0 round-of-16 win against Portugal on Sunday and coach Roberto Martinez will make last-minute decisions.
Italy skipper Giorgio Chiellini is back in contention for the match in Munich on Friday night after missing his side's previous two games – wins against Wales, in their last group match, and against Austria.
The Swiss will be without suspended captain Granit Xhaka after the Arsenal midfielder received his second booking of the tournament in the thrilling penalty shoot-out win against France.
The winners of Friday's quarter-finals will meet in the first semi-final at Wembley on Tuesday, with the second last-four tie taking place at the same venue the following day.
Italy have set a new national record of 31 games unbeaten going back to October 2018, beating the mark set by Vittorio Pozzo's World Cup and Olympic champions of the 1930s. That includes wins in their last 12 games, without conceding a goal until Austria's extra-time consolation on Saturday.
Their opponents are not far behind, though – Belgium are 13 games unbeaten, winning 11, and have lost only to England in the Nations League since the start of 2019. In 27 games each in that timeframe Italy have won 24 and drawn three, scored 80 goals and conceded seven, compared to Belgium's 23 wins, three draws and one loss, 81 goals scored and 15 conceded.
Quote of the day
Three Lions seek 'edge'
Gareth Southgate urged his players to get back in "performance state" as preparations continued for Saturday's quarter-final against Ukraine in Rome.
England travel to the Italian capital knowing it will be their only trip away from Wembley as they look to clinch a place in the semi-finals against the Czech Republic or Denmark.
The Three Lions lifted the nation by defeating Germany on Tuesday, but Southgate is keen his players retain their "edge".
Southgate said: "It's Saturday now for us, the messages are great, the congratulations are great, but they're also dangerous because it can take an edge from you and we've got to get that edge in our feeling now to get back into performance state."
England will know who they could face in the last four before their game at the Olympic Stadium against Ukraine kicks off at 8pm on Saturday as Denmark's quarter-final against the Czech Republic is a 5pm kick-off in Baku.
Post of the day
Switzerland v Spain (Quarter-final, July 2, St Petersburg, 1700 BST)
Belgium v Italy (Quarter-final, July 2, Munich, 2000 BST)