The singer-and-actor – who plays teacher Will Schuester in the musical US TV series – believes the 'Parachute' hitmaker could resurrect her career in the US following her shock firing from 'The X Factor' if she landed a role on the show.
He said: "Cheryl is on the front of every newspaper and magazine in the UK. It's not the same in America but I think she can crack it. She's a talented girl.
"Appearing on 'Glee' would be a good way for Cheryl to crack America. She was part of Fox when she was in America and they also make 'Glee'. Maybe she will get an appearance – you never know."
Matthew is also keen to see British actresses Sienna Miller and Keira Knightley appear on the programme in some capacity.
He told Reveal magazine: "I'd love to get Sienna Miller on the show. Keira Knightley would also be good. She can sing right? Well, she'd be good even if she can't."