The Black Cats midfielder was overlooked by Three Lions boss Roy Hodgson for September friendlies with Switzerland and Norway but Poyet still holds belief that the hard-tackling 26-year old can push for national team selection in the future.
"Lee needs to say: 'If I keep performing the way I have been, then sooner or later I'm going to have a chance,'" said Poyet who saw Hodgson select Newcastle United's Jack Colback and Aston Villa's Fabian Delph ahead of Cattermole.
"It's up to Roy Hodgson but if I was the England manager I would definitely pick Lee because I like his character and the way he plays the game. If, like me, he was Uruguayan there is no doubt Lee would be picked for the national team, because we like that type of combative player."
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