Dyer has emerged as one of the Swans' stand-out players this season, scoring three times to help City sit second behind Chelsea in the Premier League table on goal difference.
"England has been one of those frustrating things," he told Sky Sports News. "It would be an honour to get called up and I'll never give up.
"We have made a great start and there are a couple of players here at Swansea in with a shout but we'll keep performing and working hard to make people notice.
"You can't give up. I will keep running and playing as well as I can. I don't know what goes on with the England selectors. I'm playing well and hopefully people will see that."
Swansea face co-leaders Chelsea when the domestic calendar resumes next Saturday.