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England qualified from Group B in second place behind Wales as they reached the knockout stages of Euro 2016 in France.
However, the Three Lions exited in the round of 16 after a shock 2-1 defeat to Iceland at the Stade de Nice.
Clattenburg was a referee in the Premier League for over a decade and was a FIFA-listed referee.
The 46-year-old, who was born in Consett, County Durham, was also called up by UEFA as a match official for Euro 2016.
Referees are not allowed to officiate matches that feature their respective countries during major international competitions.
Now, Clattenburg has claimed that any referee would be "lying" if they didn't hope their country was knocked out if it cleared a path to oversee a semi-final clash or final.
Both Anthony Taylor and Michael Oliver have been called up to represent England at Euro 2020 this summer.
However, Clattenburg insisted that they would need a "little bit of luck" if they are aiming to referee at the later stages of the Euros.
"For starters, you need England eliminated as quickly as possible," he wrote for The Daily Mail.
"I'm a big England fan and it will be nice to cheer them on this time because in 2016 I wanted them out to clear the way for me.
"Any referee from any country would be lying if they said otherwise -- we're all there to try to make the semis or the final."
Clattenburg was selected as the referee for Portugal's 1-0 victory over France at the Stade de France.
The ex-Premier League referee said he thought his dream to officiate a final was over due to Wales' scintillating run at Euro 2016.
Wales, then managed by Chris Coleman, defied the odds to reach the semi-finals before they suffered a 2-0 defeat to Euro 2016 winners Portugal.
"That was great for them [Wales] but if they'd got to the final my dream would have been over," Clattenburg added.
"So life as a referee at a major tournament is a bit of a rollercoaster -- I was nearly crying when Wales beat Belgium in the quarter-final!"
England will begin their Euro 2020 campaign on Sunday against Croatia at Wembley.
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