The singer-and-actor thinks the band - which includes Zayn Malik, 21, Harry Styles, 20, Louis Tomlinson, 22, Liam Payne, 20, and Niall Horan, 20 - could join the comedy drama as students attending McKinley High School in Ohio.
Matthew - who plays teacher Will Schuester - told the Daily Star newspaper: ''We have been so fortunate to have some great cameos, and to have One Direction on would be great for the show.
''They are not much older than High School age so we could have them as students. And I am sure the younger female cast members wouldn't object to their presence either.''
The 35-year-old actor and his co-star Jane Lynch (Sue Sylvester) are also hoping for media mogul Simon - whose reality show 'X Factor' helped catapult the band into the spotlight in 2010.
He explained: ''Both mine and Jane Lynch's dream cameo is Simon Cowell. So maybe the boys could bring their manager.
''It would make great TV seeing Sue Sylvester and Simon Cowell go head to head.''
Some of One Direction's songs, including 'What Makes You Beautiful' and 'Live While We're Young', have previously been performed on 'Glee' but Matthew admitted he didn't know much about the group when they used their tracks and he is astonished at how far they have come since then.
He added: ''I remember when the show covered 'What Makes You Beautiful' I had only just heard of One Direction.
''But since then they have pretty much gone one to take over the world!''
The actress thinks it would be tough to recast her character, Winifred Sanderson.
Beck wishes he'd had ''more fun'' when Kanye West invaded the stage in protest at his 2015 Grammy Awards win.
The Duffer Brothers wanted to "experiment a little bit".
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